a) as + Bs is an unbiased estimator for σ^2.
b)The minimum variance occurs when n1 = 1 and n2 = 1, which means taking a = 0 and b = 1 in the estimator as + Bs.
c)The resulting reduced variance would be Var(S_combined) = σ2 / (n1 + n2 - 2).
The variance, we need to choose values for n1 and n2 that minimize the expressions (n1 - 1)2 and (n2 - 1)2, respectively.
(a) To show that as + Bs is an unbiased estimator for σ2, we need to show that its expected value is equal to σ2.
First, let's calculate the expected value of as:
E(as) = E[(n1-1)S1] = (n1 - 1)E(S1)
Since S1 is an unbiased estimator for σ2, E(S1) = σ2.
Therefore, E(as) = (n1 - 1)σ2.
Next, let's calculate the expected value of Bs:
E(Bs) = E[(n2-1)S2] = (n2 - 1)E(S2)
Similarly, since S2 is an unbiased estimator for σ2, E(S2) = σ2.
Therefore, E(Bs) = (n2 - 1)σ2.
Now, let's calculate the expected value of as + Bs:
E(as + Bs) = E(as) + E(Bs)
= (n1 - 1)σ2 + (n2 - 1)σ2
= (n1 + n2 - 2)σ2
Since a + b = 1, we have n1 + n2 = (a + b) + (b + b) = 2.
Therefore, E(as + Bs) = (n1 + n2 - 2)σ2 = 2σ2 = σ2.
Thus, as + Bs is an unbiased estimator for σ^2.
(b) The variance of the estimator as + Bs can be calculated as follows:
Var(as + Bs) = Var(as) + Var(Bs)
= Var((n1 - 1)S1) + Var((n2 - 1)S2)
= (n1 - 1)2 Var(S1) + (n2 - 1)2 Var(S2)
To minimize the variance, we need to choose values for n1 and n2 that minimize the expressions (n1 - 1)2 and (n2 - 1)2, respectively. The minimum variance occurs when n1 = 1 and n2 = 1, which means taking a = 0 and b = 1 in the estimator as + Bs.
The optimal variance in this case would be Var(as + Bs) = (1 - 1)2 Var(S1) + (1 - 1)2 Var(S2) = 0.
(c) To suggest an even better unbiased estimator for σ2, we can use the combined sample variance of both samples:
S_combined = ((n1 - 1)S1 + (n2 - 1)S2) / (n1 + n2 - 2)
The resulting reduced variance would be Var(S_combined) = σ2 / (n1 + n2 - 2).
By combining the samples, we reduce the variance compared to using separate estimators for each sample.
To know more about variance refer here:
https://brainly.com/question/31432390#
#SPJ11
Potential customers arrive at a self-service, two-pump petrol station at a Poisson rate of 20 cars per hour. An entering customer first waits in queue and then goes to the first free pump. However, customers will not enter the station for petrol if there are already two cars in the queue. Suppose the time a customer spends at a pump is exponentially distributed with a mean of five minutes. (a) Set up a birth and death process for the number of customers in the petrol station (in service and in queue) and draw its transition rate diagram. (b) What is the fraction of potential customers that are lost? (c) What would be the fraction of potential customers that are lost if there was only a single pump, and the time a customer spends at a pump is exponentially distributed with a mean of 2.5 minutes? Assume the same that customers will not enter the station for petrol if there are already two cars in the queue. (d) Compare and comment on the results from parts (b) and (c).
Setting up a birth and death process for the number of customers in the petrol station (in service and in queue) and drawing its transition rate diagram Given, Potential customers arrive at a self-service, two-pump petrol station at a Poisson rate of 20 cars per hour.
Arrival rate = λ = 20 cars per hour Then, interarrival time = 1/λ = 1/20 hour = 3 minutes Mean service time = 5 minutes Therefore, service rate = μ = 1/5 cars per minute Therefore, service rate = μ = 12 cars per hour The system has a maximum queue length of 2, which means that no cars will enter the station if there are already two cars in the queue. This results in a rejection rate of (20-12)/(20) = 0.4 or 40%.Therefore, λ` = λ (1-p) = 20(1-0.4) = 12 cars per hour = 0.2 cars per minute The birth and death process can be represented as follows: The transition rate diagram is shown below:(b) Calculation of the fraction of potential customers that are lost The loss rate (rejection rate) is 0.4 or 40%.
Therefore, the fraction of potential customers that are lost is 0.4 or 40%.(c) Calculation of the fraction of potential customers that are lost if there was only a single pump, and the time a customer spends at a pump is exponentially distributed with a mean of 2.5 minutes. Assume the same that customers will not enter the station for petrol if there are already two cars in the queue. The service rate is given as μ = 1/2.5 = 0.4 cars per minute, which is 24 cars per hour. Using Little's Law, the average number of cars in the system = L = λW, where W is the average time spent in the system.
To know more about Poisson rate visit:
https://brainly.com/question/17280826
#SPJ11
The line (1) has a direction vector (1,3,7). Find the magnitude of the direction vector. Select one: O a. √59 b. √56 OC √24 d. 11 e. 122
The magnitude of the direction vector (1,3,7) is √59. The magnitude of a vector represents its length or size. To find the magnitude of a vector, we use the formula:
|v| = √(v₁² + v₂² + v₃²)
For the given direction vector (1,3,7), we substitute the corresponding components into the formula:|v| = √(1² + 3² + 7²) = √(1 + 9 + 49) = √59 Therefore, the magnitude of the direction vector (1,3,7) is √59.
The magnitude of a vector is calculated by taking the square root of the sum of the squares of its components. In this case, we have a direction vector (1,3,7). To find the magnitude, we square each component and then take the square root of their sum.
For the given direction vector (1,3,7), the calculation is as follows:
Magnitude = √(1² + 3² + 7²) = √(1 + 9 + 49) = √59. Thus, the magnitude of the direction vector (1,3,7) is √59.
Learn more about vector here: brainly.com/question/9580468
#SPJ11
A bottler of drinking water fills plastic bottles with a mean volume of 999 milliliters (mL) and standard deviation 4 ml. The fill volumes are normally distributed. What proportion of bottles have volumes greater than 994 mL.?
1.0000
0.8944
0.9599
0.8925
Given data Mean volume of bottles, μ = 999 ml
Standard deviation, σ = 4 ml
Probability that the volume of bottle is greater than 994 ml, P(X > 994)We can use the standard normal distribution formula which is given as follows:Z = (X - μ) / σ
Where X is the random variable for which we need to calculate probability and Z is the standard normal variable.For P(X > 994)
,Z = (X - μ) / σ
= (994 - 999) / 4
= -1.25
Now using standard normal distribution table, we can find P(Z > -1.25)P(Z > -1.25) = 0.8944
Therefore, the Proportion of bottles that have volumes greater than 994 mL is approximately 0.8944.
Therefore, the correct option is 0.8944.
To know more about Volume visit :-
https://brainly.com/question/14197390
#SPJ11
Given the two functions f(x) = √2x - 4 and g(x) = |x| Determine the domain of (fog)(x)
The domain of (f ∘ g)(x) is [0, +∞).
To determine the domain of (f ∘ g)(x), we need to consider the compositions of the functions f(x) and g(x).
The composition (f ∘ g)(x) means we evaluate the function f(x) after applying the function g(x). In other words, we substitute g(x) into f(x).
Given:
f(x) = √(2x) - 4
g(x) = |x|
Let's find the composition (f ∘ g)(x):
(f ∘ g)(x) = f(g(x)) = f(|x|)
To determine the domain of (f ∘ g)(x), we need to find the values of x for which the composition is defined.
In the function g(x) = |x|, the absolute value function is defined for all real numbers. So there are no restrictions on the domain of g(x).
For the function f(x) = √(2x) - 4, the square root function is defined for non-negative values of the argument. Therefore, 2x must be greater than or equal to zero:
2x ≥ 0
x ≥ 0/2
x ≥ 0
Since g(x) = |x| is defined for all real numbers, and f(x) = √(2x) - 4 is defined for x ≥ 0, the composition (f ∘ g)(x) is defined for x ≥ 0.
Therefore, the domain of (f ∘ g)(x) is [0, +∞).
Visit here to learn more about domain brainly.com/question/30133157
#SPJ11
This problem has multiple parts. Each part is a subtlety different from the other, with possibly a very different answer. - You draw two card at once from a deck of 52 cards. What's the probability that at least one of them is a Heart? - You draw a card from a deck of 52 cards, see what it is and then place it back in the deck and draw a second card. What's the probability that at least of them is a Heart? - You draw two cards from a deck of 52 cards. What's the probability that both of them are Hearts if the finst one is a Heart?
The probabilities for each scenario are as follows: (a) the probability of drawing at least one Heart is 1 - (the probability of drawing no Hearts), (b) the probability of drawing at least one Heart is 1 - (the probability of drawing no Hearts in two consecutive draws), and (c) the probability of both cards being Hearts, given that the first card is a Heart, is the probability of drawing a Heart on the second draw.
(a) In the first scenario, the probability of drawing at least one Heart can be found by calculating the complement of drawing no Hearts. The probability of drawing no Hearts is (39/52) * (38/51) since there are 39 non-Heart cards remaining out of 52 total cards on the first draw, and 38 non-Heart cards remaining out of 51 total cards on the second draw.
Therefore, the probability of drawing at least one Heart is 1 - [(39/52) * (38/51)].
(b) In the second scenario, since the first card drawn is replaced back into the deck before drawing the second card, the probability of drawing at least one Heart on the second draw is the complement of drawing no Hearts on both draws.
The probability of drawing no Hearts on both draws is (39/52) * (39/52) since the probability of drawing a non-Heart on each draw is 39/52. Therefore, the probability of drawing at least one Heart is 1 - [(39/52) * (39/52)].
(c) In the third scenario, we are given that the first card drawn is a Heart. Since the first card is a Heart, there are now 51 cards remaining, including 12 Hearts. Therefore, the probability of drawing a Heart on the second draw is 12/51.
Visit here to learn more about probability:
brainly.com/question/13604758
#SPJ11
Although the phenomenon is not well understood, it
appears that people born during the winter months are
slightly more likely to develop schizophrenia than
people born at other times (Bradbury & Miller, 1985).
The following hypothetical data represent a sample of
50 individuals diagnosed with schizophrenia and a
sample of 100 people with no psychotic diagnosis.
Each individual is also classified according to season
in which he or she was born. Do the data indicate a
significant relationship between schizophrenia and the
season of birth? Test at the .05 level of significance.
Season of Birth
Summer Fall Winter Spring
No Disorder Schizophrenia 26 24 22 28 9 11 18 12 a. 35
b. 40
c. 0
The task is to determine if there is a significant relationship between schizophrenia and the season of birth based on the provided data. The data consists of a sample of 50 individuals diagnosed
To determine if there is a significant relationship between schizophrenia and the season of birth, a statistical test needs to be conducted on the given data.
The data includes counts of individuals with schizophrenia and without a psychotic diagnosis for each season of birth. To test for significance, a chi-square test can be employed to assess the association between the variables.
The test will compare the observed frequencies in each season with the expected frequencies under the assumption of no relationship between the variables.
By comparing the obtained chi-square value with the critical value at a significance level of .05, it can be determined if the relationship between schizophrenia and season of birth is statistically significant.
Careful calculations and interpretation of the results are necessary to make a conclusive determination.
Learn more about Statistics: brainly.com/question/12805356
#SPJ11
The following data represent the length of time, in days, to recovery for patients randomly treated with one of two medications to clear up severe bladder infections. Find a
90% confidence interval for the difference μ2−μ1 between in the mean recovery times for the two medications, assuming normal populations with equal variances.
Medication 1
n1=10
x1=16
s21=1.7
Medication 2
n2=17
x2=19
s22=1.5
The 90% confidence interval for the difference μ2−μ1 between in the mean recovery times for the two medications is given as follows:
(1.93, 4.07).
How to obtain the confidence interval?The difference of the means is given as follows:
19 - 16 = 3.
The standard error for each sample is given as follows:
[tex]s_1 = \frac{1.7}{\sqrt{10}} = 0.54[/tex][tex]s_2 = \frac{1.5}{\sqrt{17}} = 0.36[/tex]Hence the standard error for the distribution of differences is given as follows:
[tex]s = \sqrt{0.54^2 + 0.36^2}[/tex]
s = 0.649
Looking at the z-table, the critical value for a 90% confidence interval is given as follows:
z = 1.645.
The lower bound of the interval is given as follows:
3 - 1.645 x 0.649 = 1.93.
The upper bound of the interval is given as follows:
3 + 1.645 x 0.649 = 4.07.
More can be learned about the z-distribution at https://brainly.com/question/25890103
#SPJ4
Every day you are visiting a convenient store. On the way to the store, you need to cross the street at a crossing with a traffic light. The traffic light works in the mode: red light (for pedestrian) is "on" for 170 seconds, green light (for pedestrian) is "on" for 30 seconds. How many seconds on average do you stand at this traffic light? (We believe that you cross the road only to green, and do it instantly). Average time = ? sec To round the answer to the second decimal: 0.01
The average time you stand at the traffic light is approximately 145 seconds, rounded to the nearest second.
To calculate the average time you stand at the traffic light, we need to consider the probabilities of encountering each light. The red light is on for 170 seconds, while the green light is on for 30 seconds. Since we assume you only cross when the green light is on, the average time can be calculated as follows:
Average time = (Probability of encountering red light) * (Duration of red light) + (Probability of encountering green light) * (Duration of green light)
The probability of encountering the red light can be calculated by dividing the duration of the red light by the total duration of both lights:
Probability of encountering red light = Duration of red light / (Duration of red light + Duration of green light)
Probability of encountering red light = 170 / (170 + 30) = 170 / 200 = 0.85
Similarly, the probability of encountering the green light can be calculated:
Probability of encountering green light = Duration of green light / (Duration of red light + Duration of green light)
Probability of encountering green light = 30 / (170 + 30) = 30 / 200 = 0.15
Now we can calculate the average time:
Average time = (0.85 * 170) + (0.15 * 30) = 144.5 seconds
Rounded to the nearest second, the average time you stand at the traffic light is 145 seconds.
Therefore, the average time is 145 seconds (rounded to the nearest second).
To know more about probability refer here:
https://brainly.com/question/31828911#
#SPJ11
Evaluate the integral or state that it diverges. X S- -dx 4 (x+4)² *** Select the correct choice and, if necessary, fill in the answer box to complete your choice. OA. The integral converges to OB. The integral diverges.
The integral diverges, the integral converges if the function being integrated approaches 0 as the upper limit approaches infinity.
In this case, the function f(x)=−4(x+4)
2
does not approach 0 as x approaches infinity. In fact, it approaches negative infinity. This means that the integral diverges.
Here is a Python code that shows how to evaluate the integral:
Python
import math
def integral(x):
return -4 * (x + 4) ** 3 / 3
print(integral(100))
The output of this code is -1499818.6666666667. This shows that the integral does not converge to a specific value. Instead, it approaches negative infinity as the upper limit approaches infinity.
To know more about function click here
brainly.com/question/28193995
#SPJ11
In southern California, a growing number of persons pursuing a teaching credential are choosing paid internships over traditional student teaching programs. A group of eleven candidates for three teaching positions consisted of eight paid interns and three traditional student teachers. Assume that all eleven candidates are equally qualified for the three positions, and that x represents the number of paid interns who are hired. (a) Does x have a binomial distribution or a hypergeometric distribution? Support your answer. (Round your answer to four decimal places.) - hypergeometric - binomial
(b) Find the probability that three paid interns are hired for these positions. (Round your answer to four decimal places.) (c) What is the probability that none of the three hired was a paid intern? (Round your answer to four decimal places.) (d) Find P(x ≤ 1).
(a) The distribution is hypergeometric because candidates are selected without replacement. (b) Probability of hiring three paid interns is approximately 0.0533. (c) Probability of none hired being paid interns is approximately 0.0727. (d) P(x ≤ 1) is approximately 0.2061.
(a) The situation described in the problem involves selecting a specific number of candidates from a group without replacement, which suggests a hypergeometric distribution. In this case, there are two distinct groups: the paid interns and the traditional student teachers, and the goal is to select three candidates from this combined group. (b) To find the probability of three paid interns being hired, we need to calculate the probability of selecting three paid interns from the group of eleven candidates. The probability can be calculated using the hypergeometric distribution formula:P(X = 3) = (C(8, 3) * C(3, 0)) / C(11, 3) ≈ 0.0533
(c) The probability that none of the three hired candidates are paid interns is equivalent to selecting three traditional student teachers. Therefore, we calculate the probability using the hypergeometric distribution:
P(X = 0) = (C(3, 0) * C(8, 3)) / C(11, 3) ≈ 0.0727
(d) To find P(x ≤ 1), we need to calculate the probability of selecting either zero or one paid intern. We can use the cumulative probability formula for the hypergeometric distribution:
P(x ≤ 1) = P(x = 0) + P(x = 1) = (C(3, 0) * C(8, 3)) / C(11, 3) + (C(3, 1) * C(8, 2)) / C(11, 3) ≈ 0.2061
Therefore, (a) The distribution is hypergeometric because candidates are selected without replacement. (b) Probability of hiring three paid interns is approximately 0.0533. (c) Probability of none hired being paid interns is approximately 0.0727. (d) P(x ≤ 1) is approximately 0.2061.
To learn more about probability click here
brainly.com/question/14210034
#SPJ11
Consider two independent Bernoulli r.v., U and V, both with probability of success 1/2. Let X=U+V and Y=∣U−V∣. (a) Calculate the covariance of X and Y,σ X,Y
. (b) Are X and Y independent? Justify your answer. c) Find the random variable expressed as the conditional expectation of Y given X, i.e., E[Y∣X]. If it has a "named" distribution, you must state it. Otherwise support and pdf is enough.
The random variable expressed as the conditional expectation of Y given X is E[Y|X]=1/2(X−Y).
Two independent Bernoulli r.v., U and V, both with probability of success 1/2. Let X=U+V and Y=∣U−V∣.To calculateThe covariance of X and Y (σX,Y) and if X and Y are independent and the random variable expressed as the conditional expectation of Y given X, i.e., E[Y∣X].Solution(a) Calculation of covariance of X and Y, σX,YUsing the properties of covariance, we have: σX,Y=E[XY]−E[X]E[Y].
Using the expectation calculated above, we can now find the covariance of X and Y as follows:σX,Y=E[XY] Thus, the covariance of X and Y is σX,Y=3/4.(b) Checking independence of X and Y In order to show that X and Y are independent, we need to show that their covariance is zero, i.e., σX,Y=0.
To know more about variable visit:
https://brainly.com/question/16906863
#SPJ11
A statistician wished to test the claim that the variance of the nicotine content (measured in milligram) in the cigarette is 0.723. She selected a random sample of 24 cigarettes and found the standard deviation of 1.15 milligram and the population from which the sample is selected is assumed to be (approximately) normally distributed. At 0.01 level of significance, is there enough evidence to accept the statistician's claim? In your hypothesis testing, (a) state (C1) the null hypothesis and alternative hypothesis. Indicate (C1) the correct tailed test to be used. (b) determine (C1) the distribution that can be used and give (C1) your reason. (1 mark) (c) use (C3) the critical value approach to help you in decision making. (9.5 marks) (d) write (C3) your conclusion. (1.5 marks)
a) The null hypothesis (H0) would be that the variance of the nicotine content in cigarettes is equal to 0.723 milligram squared.
The alternative hypothesis (Ha) would be that the variance is not equal to 0.723 milligram squared.
b) There is enough evidence to accept the statistician's claim that the variance of the nicotine content in cigarettes is 0.723.
a) The null hypothesis (H0) would be that the variance of the nicotine content in cigarettes is equal to 0.723 milligram squared.
The alternative hypothesis (Ha) would be that the variance is not equal to 0.723 milligram squared.
b) In this case, we can use the chi-square distribution to test the hypothesis since we are dealing with the variance and the sample size is relatively small (n = 24).
c) For the critical value approach, we need to calculate the chi-square test statistic and compare it to the critical value from the chi-square distribution at a significance level of 0.01.
The test statistic (chi-square) can be calculated using the formula:
chi-square = (n - 1) sample variance / population variance
In this case:
n = 24 (sample size)
sample variance = 1.3225
population variance = 0.723
So, chi-square = (24 - 1) 1.3225 / 0.723 = 42.0712
degrees of freedom (df) equal to (n - 1) = 23.
So, the critical value for a significance level of 0.01 and 23 degrees of freedom is 41.6383.
Since the calculated chi-square value (42.0712) is greater than the critical value (41.6383), we can reject the null hypothesis.
Therefore, at a 0.01 level of significance, there is enough evidence to accept the statistician's claim that the variance of the nicotine content in cigarettes is 0.723.
Learn more about Hypothesis here:
https://brainly.com/question/29576929
#SPJ4
Patrick won a sweepstakes and will receive money each week for 52 weeks. The first week he will receive $10. Every week after that he will receive 10% more than he got the previous week. How much money did he receive over the 52 weeks?
Patrick received a total of approximately $6,785.97 over the course of 52 weeks.
To calculate the total amount of money Patrick received over the 52 weeks, we can use the concept of a geometric sequence. The first term of the sequence is $10, and each subsequent term is 10% more than the previous term.
To find the sum of a geometric sequence, we can use the formula:
Sn = a * (r^n - 1) / (r - 1),
where Sn is the sum of the first n terms, a is the first term, r is the common ratio, and n is the number of terms.
In this case, a = $10, r = 1 + 10% = 1.1 (common ratio), and n = 52 (number of weeks).
Plugging these values into the formula, we can calculate the sum of the sequence:
S52 = 10 * (1.1^52 - 1) / (1.1 - 1)
After evaluating this expression, we find that Patrick received approximately $6,785.97 over the 52 weeks.
As a result, Patrick collected about $6,785.97 in total over the course of 52 weeks.
for such more question on total amount
https://brainly.com/question/19079438
#SPJ8
A ternary string is a sequence of digits, where each digit is either 0, 1, or 2. For example "011202" is a ternary string of length 6. How many ternary strings of length n have at least four 0s? Explain your answer.
A ternary string is a sequence of digits, where each digit is either 0, 1, or 2. For example "011202" is a ternary string of length 6.
How many ternary strings of length n have at least four 0s? Explain your answer.
To find the number of ternary strings of length n that have at least four 0s, we need to consider two cases: strings with exactly four 0s and strings with more than four 0s.
The total number of ternary strings of length n is 3^n, and the number of strings with exactly four 0s is given by the binomial coefficient C(n, 4). Therefore, the number of strings with at least four 0s is the sum of these two cases: C(n, 4) + C(n, 5) + C(n, 6) + ... + C(n, n).
A ternary string of length n can have 0, 1, 2, ..., or n 0s. To count the number of strings with exactly four 0s, we need to choose four positions out of the n positions to place the 0s, and the remaining positions can be filled with either 1s or 2s. The number of ways to choose four positions out of n is given by the binomial coefficient C(n, 4).
Similarly, for strings with more than four 0s, we need to choose five positions, six positions, and so on, up to n positions for the 0s. The number of ways to choose k positions out of n is given by C(n, k), where k ranges from 5 to n.
Therefore, the total number of ternary strings of length n with at least four 0s is the sum of all these cases: C(n, 4) + C(n, 5) + C(n, 6) + ... + C(n, n).
Note that C(n, k) represents the number of ways to choose k items out of n, and it is computed as C(n, k) = n! / (k!(n-k)!).
By summing up these binomial coefficients, we obtain the final answer for the number of ternary strings of length n that have at least four 0s.
To learn more about number click here:
brainly.com/question/3589540
#SPJ11
Part 1: Practice with the Big Ideas At certain points during the COVID-19 pandemic, many of us had no choice but to complete our work from home. For some employees, working from home was so rewarding that they found themselves wishing they could work from home indefinitely. One report, in fact, claimed that 75% of workers with jobs that could be done from home said that if they had a choice, they'd like to continue working from home all or most of the time, even when it's safe for them to work outside of their home. Believing this claimed value is too high, a researcher surveys a random sample of 945 adult employees and finds that 693 of them would like to continue working from home all or most of the time after COVID-19 restrictions case. 1.If we want to use the above information to conduct a hypothesis test, we need to begin with two competing hypotheses. The first hypothesis is the initial claim to be tested about the population. We would write this claim as Ip-0.75. What do we call this hypothesis? 2. The second hypothesis we begin with illustrates our theory, or what we believe is actually going on in the population (ie, the reason we are conducting the hypothesis test in the first place). Here, we would write this second hypothesis as 1, p<0.75. What do we call this hypothesis? Look carefully at the hypotheses above, within Questions 1 and 2. Notice that both hypotheses include the symbol "p What does "p" stand for? Look again at the hypothesis presented within Question 2. Notice that there is a " (or less than) sign within that hypothesis Why exactly would we be using the sign as opposed to the "" (or greater than) sign? Before we can conduct our hypothesis test, we need to determine the sample proportion. Recall that 945 employees were surveyed, and 693 of them said they would like to continue working from home all or most of the time. What will the sample proportion (or) be? Please compute this value below and round your answer to three decimal places To be able to conduct a hypothesis test, we will now need to compute a test statistic (using the following formula) Please attempt to compute this test statistic below, showing as much work as you can.
1. The first hypothesis is called the null hypothesis (H₀), which states that the proportion of employees who want to continue working from home is equal to 0.75 (Ip = 0.75).
2. The second hypothesis is called the alternative hypothesis (H₁), which states that the proportion of employees who want to continue working from home is less than 0.75 (p < 0.75).
In this context, "p" stands for the population proportion of employees who want to continue working from home.
The alternative hypothesis (H₁) uses the "less than" sign because the researcher believes that the claimed value of 75% is too high, indicating a lower proportion of employees who want to continue working from home.
To compute the sample proportion (or), we divide the number of employees who want to continue working from home (693) by the total sample size (945):
or = 693/945 = 0.732 (rounded to three decimal places).
To compute the test statistic, we use the formula:
z = (or - Ip) / sqrt((Ip * (1 - Ip)) / n)
where or is the sample proportion, Ip is the hypothesized population proportion, and n is the sample size.
To learn more about hypothesis click on:brainly.com/question/32298676
#SPJ11
A survey was given to 200 residents of the state of Florida. They were asked to state how much they spent on online in the past month. What type of graph would you use to look at the responses? You want to describe the shape and spread of the data. pie chart bar chart histogram contingency table
When it comes to visualizing data for continuous variables like the money spent on online shopping, histograms are a great choice. Therefore, a histogram would be used to look at the responses in this case. The shape and spread of the data can be described as follows:
Symmetrical (normal) distribution - a histogram with a bell-shaped curve is said to be symmetrical or normally distributed. This is due to the fact that the data is equally distributed on either side of the mean of the data set. Skewed distribution - when one tail is longer than the other, the distribution is referred to as skewed. When the tail is longer on the left, it is said to be left-skewed, while when it is longer on the right, it is right-skewed. Bimodal distribution - when a histogram has two peaks or modes, it is said to be bimodal.
This could occur, for example, if there are two distinct groups in a data set. Spread of data The spread of a histogram can be described as: Symmetrical distribution - In a symmetrical distribution, the spread is determined by the standard deviation, which is the same on both sides of the mean. Skewed distribution - When a histogram is skewed, the spread is determined by the distance between the median and the tails. Bimodal distribution - In a bimodal distribution, the spread is determined by the distance between the two peaks.
To know more about residents visit:-
https://brainly.com/question/33125432
#SPJ11
In 2018 it was estimated that approximately 43% of the American population watches the Super Bowl yearly. Suppose a sample of 137 Americans is randomly selected. After verifying the conditions for the Central Limit Theorem are met, find the probability that the majority (more than 50% ) watched the Super Bowl. First, verify that the conditions of the Central Limit Theorem are met. The Random and Independent condition h The Large Samples condition holds. The Big Populations condition reasonably be assumed to hold. The probability is (Type an integer or decimal rounded to three decimal places as needed.)
The probability that the majority of the sample (more than 50%) watched the Super Bowl is approximately 0.076, or 7.6%.
To verify the conditions for the Central Limit Theorem (CLT) are met, we need to check the random and independent condition, the large samples condition, and the big populations condition.
Random and Independent Condition:
We assume that the sample of 137 Americans is randomly selected, meaning each individual has an equal chance of being included in the sample. Additionally, if the sample size is less than 10% of the population, it can be considered independent. Since the American population is much larger than 137, we can assume this condition is met.
Large Samples Condition:
The large samples condition states that the sample size should be sufficiently large for the CLT to apply. There is no specific threshold for this condition, but a commonly used guideline is that the sample size should be at least 30. In this case, the sample size is 137, which is greater than 30, so we can assume this condition is met.
Big Populations Condition:
The big populations condition assumes that the population from which the sample is drawn is much larger than the sample itself. Since the American population is quite large, we can reasonably assume this condition is met.
Now that we have verified the conditions for the CLT are met, we can proceed to find the probability that the majority (more than 50%) of the sample watched the Super Bowl.
Since the proportion of Americans who watch the Super Bowl yearly is estimated to be 43%, the probability of an individual in the sample watching the Super Bowl is also 0.43.
The distribution of the sample proportion (p-hat) will be approximately normal with a mean equal to the population proportion (p) and a standard deviation (sigma) given by:
sigma = sqrt((p * (1 - p)) / n)
where n is the sample size.
In this case, n = 137 and p = 0.43.
Calculating the standard deviation:
sigma = sqrt((0.43 * (1 - 0.43)) / 137) ≈ 0.049
To find the probability that the majority watched the Super Bowl (more than 50%), we need to calculate the z-score and find the area under the normal curve corresponding to the z-score.
The z-score formula is:
z = (x - μ) / sigma
where x is the value of interest, μ is the mean, and sigma is the standard deviation.
In this case, we want to find the probability that the sample proportion is greater than 0.50, so:
z = (0.50 - 0.43) / 0.049 ≈ 1.43
Using a standard normal distribution table or calculator, we can find the probability corresponding to the z-score of 1.43. The area to the left of 1.43 is approximately 0.9236.
Since we're interested in the probability that the majority (more than 50%) watched the Super Bowl, we subtract the area to the left from 1:
Probability = 1 - 0.9236 ≈ 0.076
Therefore, the probability that the majority of the sample (more than 50%) watched the Super Bowl is approximately 0.076, or 7.6%.
Learn more about sample here:
https://brainly.com/question/32907665
#SPJ11
Knowledge/Understanding (8 marks) Identify the choice that best completes the statement ar answers the question. 1. A line passes through the points A(2,3) and B(−2,1). Find a vector equation of the line. a. [x,y]=[2,3]+t[−2,1] c. [x,y]=[−4,−2]+t[2,3] b. [x,y]=[−2,1]+i[2,3] d. [x,y]=[2,3]+t[−4,−2] 2. A line has slope −3 and y-intereept 5 . Find a vector equation of the line. a. [x,y]=[0,5]+t[1,−3] c. [x,y]=[1,−3]+t[0,5] b. [x,y]=[5,0]+t[0,−3] d. [x,y]=[−3,5]+t[−3,−3] 3. Write the scalar equation of the plane with normal vector n
=[1,2,1] and passing through the point (3,2,1). a. x+2y+z+8=0 b. x+2y+z−8=0 c. 3x+2y+z−8=0 d. 3x+2y+z+8=0 4. A plane passes through the origin and has the direction vectors [1,2,3] and [−1,3,−2]. Find a scalar equation of the plane: a. x+2y+3z=0 c. 13x+y−5z=9 b. −x+3y−2z=0 d. 13x+y−5z=0 5. The parametric ⎩
⎨
⎧
x=s+t
y=1+t. Find a scalar equation of the plane. z=1−s
a. b. x−y+z+2=0
x−y+z−2=0
c. x+y+z=0 d. x−y+z=0 6. Find the intersection point of the two lines: { x=1+t
y=−1+t
and { x=5−t
y=4−2t
. a. (5,4) c. (1,−1) b. (1,1) d. (4,2) 7. In three-space, find the intersection point of the two lines: [x,y,z]=[1,1,2]+{[0,1,1] and [x,y,z]=[−5,4,−5] +t[3,−1,4]. a. (−5,4,−5) c. (1,1,2) b. (1,2,3) d. (3,2,1) a. (−7,−7,−3) c. (2,−1,0) b. (1,−3,−3) d. (2,1,−3)
1. a The vector equation of a line passing through the points A(2,3) and B(−2,1) is: [x, y] = [2, 3] + t[−2, 1] = [2 − 2t, 3 − t]
So the answer is a
2. a
A line with slope −3 and y-intercept 5 can be represented by the vector equation:
[x, y] = [0, 5] + t[1, −3] = [t, 5 − 3t]
So the answer is a
3.b
The scalar equation of the plane with normal vector n = [1, 2, 1] and passing through the point (3, 2, 1) is:
n · (x − 3) + n · (y − 2) + n · (z − 1) = 0
or
x + 2y + z − 8 = 0
So the answer is b
4.d
The plane passes through the origin and has the direction vectors [1, 2, 3] and [−1, 3, −2]. The cross product of these two vectors is the normal vector of the plane: n = [1, 2, 3] × [−1, 3, −2] = [13, 1, −5]
The scalar equation of the plane is:
13x + y − 5z = 9
So the answer is d
5. c
The parametric equations of the plane are:
x = s + t
y = 1 + t
z = 1 − s
To find a scalar equation of the plane, we can take the cross product of the two direction vectors: n = (1, 1, −1) × (1, 0, 1) = 2 * (0 − 1) = −2
The scalar equation of the plane is:
x − y + 2z = 0
So the answer is c
6. b
The two lines intersect when the two sets of parametric equations are equal. Setting the x and y components equal, we get:
1 + t = 5 − t
−1 + t = 4 − 2t
Solving these equations, we get t = 2 and t = −1. The intersection point for t = 2 is (5, 4), and the intersection point for t = −1 is (1, −1). The answer is **b**.
7.b
The two lines intersect when the two sets of parametric equations are equal. Setting the x, y, and z components equal, we get:
1 + 0t = −5 + 3t
1 + 1t = 4 − 1t
2 + 1t = −5 + 4t
Solving these equations, we get t = 1/2. The intersection point is then (1, 2, 3). The answer is **b**.
To know more about equation click here
brainly.com/question/649785
#SPJ11
Determine whether the function has an inverse, (b) graph f and
f −1
in the same coordinate plane, (c) find the domain and range of f and f −1
, (d) find its inverse f −1
, and (e) find derivative of f −1
. f(x)=log 2
(x−5)+1.
The given function is f(x) = log2(x - 5) + 1.Let y = f(x) .Then, y = log2(x - 5) + 1 To find the inverse, let x = f(y).Then, x = log2(y - 5) + 1.We need to solve this equation for y and then interchange x and y.f(y) = log2(y - 5) + 1 - 1= log2(y - 5)
The domain of the given function is (5, ∞) and the range of the given function is R.Let's calculate the inverse function by exchanging x and y in the above equation.x = log2(y - 5)x = log2(y - 5)2^x = y - 5y = 2^x + 5 Therefore, the inverse function of f(x) is f^(-1)(x) = 2^x + 5.The derivative of the inverse function is f'(x) = d/dx [2^x + 5]= (ln 2) * 2^x.(b) Graph of f and f^(-1):From the graph, it is evident that f and f^(-1) are symmetric about the line y = x.(c) Domain and Range of f and f^(-1):The domain of the given function is (5, ∞) and the range of the given function is R.The domain of f^(-1)(x) is R and the range of f^(-1)(x) is (5, ∞).(d) Inverse of f(x):The inverse of the function f(x) is f^(-1)(x) = 2^x + 5.(e) Derivative of f^(-1)(x):The derivative of the inverse function is f'(x) = d/dx [2^x + 5]= (ln 2) * 2^x.
Therefore, the given function has an inverse, its inverse is f^(-1)(x) = 2^x + 5 and the derivative of its inverse function is f'(x) = (ln 2) * 2^x.
To learn more about domain visit:
brainly.com/question/13113489
#SPJ11
(x^\frac{1}{2} +1)(x^\frac{1}{2} -1)
[tex](x^\frac{1}{2} +1)(x^\frac{1}{2} -1)[/tex]
Answer:
x-1
Step-by-step explanation:
To simplify the expression (x^(1/2) + 1)(x^(1/2) - 1), we can use the difference of squares formula, which states that a^2 - b^2 = (a + b)(a - b).
In this case, let's rewrite the expression as follows:
(x^(1/2) + 1)(x^(1/2) - 1) = [(x^(1/2))^2 - 1^2]
Using the difference of squares formula, we have:
[(x^(1/2))^2 - 1^2] = (x^(1/2) + 1)(x^(1/2) - 1)
Therefore, the simplified expression is x - 1.
A banker commutes daily from his apartment to his midtown office. The average time for a one-way trip is 20 minutes, with a standard deviation of 4.8 minutes. Assume the trip times to be normally distributed. (a) If the office opens at 9:00 A.M. and the banker leaves his apartment at 8:45 A.M. daily, what percentage of the time is he late for work? (b) Find the probability that 2 of the next 4 trips will take at least 1/2 hour.
The banker is late for work approximately 14.92% of the time.
The probability that 2 out of the next 4 trips will take at least 30 minutes is approximately 0.0091 or 0.91%.
To solve these problems, we can use the properties of the normal distribution and Z-scores. Let's calculate the answers step by step.
(a) To find the percentage of the time the banker is late for work, we need to calculate the probability that his trip time exceeds 15 minutes (since he leaves at 8:45 A.M.).
Calculate the Z-score for a trip time of 15 minutes.Z = (x - μ) / σ
where x is the trip time, μ is the mean trip time, and σ is the standard deviation.
Z = (15 - 20) / 4.8
Z ≈ -1.042
Look up the corresponding probability from the Z-table.Using a standard normal distribution table or calculator, we find that the probability corresponding to Z = -1.042 is approximately 0.1492.
Convert the probability to a percentage.Percentage = 0.1492 * 100 ≈ 14.92%
Therefore, the banker is late for work approximately 14.92% of the time.
(b) To find the probability that 2 out of the next 4 trips will take at least 30 minutes, we can use the binomial distribution. Let's break it down step by step.
Calculate the probability of a trip taking at least 30 minutes.First, let's convert 30 minutes to Z-score:
Z = (30 - 20) / 4.8
Z ≈ 2.083
Now, let's find the corresponding probability using the Z-table:
Probability = 1 - probability(Z ≤ 2.083)
Probability = 1 - 0.9811
Probability ≈ 0.0189
Calculate the probability of exactly 2 out of 4 trips taking at least 30 minutes.Using the binomial distribution formula, we can calculate the probability for exactly 2 successes (trips taking at least 30 minutes) out of 4 trials (total trips):
P(X = 2) = (4 C 2) *[tex](0.0189)^2 *[/tex] [tex](1 - 0.0189)^(4 - 2)[/tex]
P(X = 2) = 6 * [tex]0.0189^2 * 0.9811^2[/tex]
P(X = 2) ≈ 0.0091
Therefore, the probability that 2 out of the next 4 trips will take at least 30 minutes is approximately 0.0091 or 0.91%.
Learn more about probability
brainly.com/question/32004014
#SPJ11
According to a recent survey, the population distribution of number of years of education for self-employed individuals in a certain region has a mean of 15.9 and a standard deviation of 2.4. a. Identify the random variable X whose distribution is described here. b. Find the mean and the standard deviation of the sampling distribution of x for a random sample of size 36. Interpret them. c. Repeat (b) for n=144. Describe the effect of increasing n.
a. The random variable X represents the number of years of education for self-employed individuals in a certain region.
b. For a random sample of size 36, the mean of the sampling distribution of X is 15.9 years and the standard deviation is 0.4 years.
c. For a random sample of size 144, the mean of the sampling distribution of X is 15.9 years and the standard deviation is 0.2 years.
The random variable X is a quantitative variable that measures the number of years of education for self-employed individuals. It represents the values that can be observed or measured in this context.
The mean of the sampling distribution is equal to the mean of the population, which in this case is 15.9 years. This means that, on average, the number of years of education in random samples of size 36 will be 15.9 years.
The standard deviation of the sampling distribution is the population standard deviation divided by the square root of the sample size. Given that the population standard deviation is 2.4 years and the sample size is 36, the standard deviation of the sampling distribution is 0.4 years.
Similar to part b, the mean of the sampling distribution is equal to the mean of the population, which remains 15.9 years. However, the standard deviation of the sampling distribution decreases as the sample size increases. For a sample size of 144, the standard deviation of the sampling distribution is calculated by dividing the population standard deviation of 2.4 years by the square root of 144, resulting in a standard deviation of 0.2 years.
Increasing the sample size reduces the variability in the sampling distribution, resulting in a smaller standard deviation. This means that larger sample sizes provide more precise estimates of the population mean, as the values in the sampling distribution are closer to the true population mean.
Learn more about Random variable
brainly.com/question/17238412
#SPJ11
A refers to Mean 1 and B refers to Mean 2: Which of the following is an example of a directional research hypothesis equation
Question 9 options:
H1: A + B
H1: A > B
H1: A = B
An example of a directional research hypothesis equation is H1: A > B. This hypothesis suggests that there is a significant difference between the means of two groups, with A being greater than B.
It implies a one-sided alternative where the researcher is specifically interested in determining if A is larger than B, rather than simply investigating whether there is a difference or equality between the means.
A directional research hypothesis equation, like H1: A > B, indicates a specific direction of the expected difference between the means. It implies that the researcher is focused on finding evidence that supports the idea of A being greater than B.
This type of hypothesis is appropriate when there is prior theoretical or empirical evidence suggesting a particular direction of the effect, or when the researcher has a specific research question or expectation about the relationship between the variables.
In contrast, H1: A + B and H1: A = B are examples of non-directional research hypothesis equations. H1: A + B suggests a general alternative that the means of A and B are not equal, without specifying the direction of the difference. H1: A = B represents a null hypothesis or a hypothesis of no difference, where the means of A and B are assumed to be equal.
Visit here to learn more about hypothesis : https://brainly.com/question/11560606
#SPJ11
The concentration of blood hemoglobin in middle-aged adult females is normally distributed with a mean of 13.5 g/dL and a standard deviation of 0.86 g/dL. Determine the hemoglobin levels corresponding to the: 90th percentile Middle 85% of middle-aged adult female hemoglobin levels Standard Normal Distribution Table
a. Hemoglobin Levels =
b. Hemoglobin Levels = to
a) The hemoglobin levels corresponding to the 90th percentile is 14.67 g/dL.
b) The hemoglobin levels that correspond to the middle 85% of middle-aged adult female hemoglobin levels are between 11.97 g/dL and 15.03 g/dL.
a. To determine the hemoglobin level corresponding to the 90th percentile, we need to use the standard normal distribution table or calculator to find the z-score that corresponds to the 90th percentile.
Using the standard normal distribution table, we find the z-score that corresponds to the 90th percentile is approximately 1.28.
We can then use the formula z = (x - μ) / σ, where z is the z-score, x is the hemoglobin level we want to find, μ is the mean of the distribution, and σ is the standard deviation.
Substituting the values we have, we get:
1.28 = (x - 13.5) / 0.86
Solving for x, we get:
x = 14.67 g/dL
Therefore, the hemoglobin levels corresponding to the 90th percentile is 14.67 g/dL.
b. To determine the hemoglobin levels that correspond to the middle 85% of middle-aged adult female hemoglobin levels, we need to find the z-scores that correspond to the 7.5th and 92.5th percentiles, which are the cutoff points for the middle 85%.
Using the standard normal distribution table, we find that the z-score that corresponds to the 7.5th percentile is approximately -1.44, and the z-score that corresponds to the 92.5th percentile is approximately 1.44.
We can then use the same formula as in part a to find the hemoglobin levels that correspond to these z-scores:
-1.44 = (x - 13.5) / 0.86
x = 11.97 g/dL
and
1.44 = (x - 13.5) / 0.86
x = 15.03 g/dL
Therefore, the hemoglobin levels that correspond to the middle 85% of middle-aged adult female hemoglobin levels are between 11.97 g/dL and 15.03 g/dL.
Learn more about percentile here:
https://brainly.com/question/1594020
#SPJ11
4. a) Plot the solid between the surfaces z = x2 +y, z = 2x b) Using triple integrals, find the volume of the solid obtained in part a) 4 If d=49, find the multiplication of d by times the value of the obtained volume. TT
Given that d = 49, multiplying d by the value of the obtained volume gives us (49)(4/3) = 196/3. Therefore, the result is 196/3 times the value of d.
To find the volume of the solid formed between the surfaces z = x^2 + y and z = 2x, we can use triple integrals. The volume can be calculated by integrating the difference between the upper and lower surfaces over the appropriate limits. After performing the integration, we find that the volume is 4/3 cubic units. If d = 49, then multiplying d by the value of the obtained volume gives us 196/3.
To begin, let's visualize the solid between the surfaces z = x^2 + y and z = 2x. In this case, the surface z = x^2 + y represents a parabolic shape that opens upward, while the surface z = 2x is a plane that intersects the paraboloid. The solid is bounded by the curves formed by these two surfaces.
To find the volume using triple integrals, we need to determine the limits of integration for each variable. Since the surfaces intersect at z = 2x, we can set up the integral using the limits of x and y. The limits for x can be determined by equating the two surfaces: x^2 + y = 2x. Rearranging this equation, we get x^2 - 2x + y = 0.
To find the limits of x, we solve this quadratic equation for x. Factoring out x, we have x(x - 2) + y = 0. Setting each factor equal to zero, we get x = 0 and x - 2 = 0, which gives x = 0 and x = 2. These are the limits for x.
For the limits of y, we need to find the bounds of y in terms of x. Rearranging the equation x^2 - 2x + y = 0, we have y = -x^2 + 2x. This represents a downward-opening parabola. To find the limits for y, we evaluate the y-coordinate of the parabola at x = 0 and x = 2.
At x = 0, y = 0, and at x = 2, y = -2^2 + 2(2) = -4 + 4 = 0. Thus, the limits for y are from 0 to 0.
Now, we can set up the triple integral to calculate the volume. The volume (V) is given by V = ∬R (2x - x^2 - y) dA, where R represents the region bounded by the limits of x and y.
Integrating the expression (2x - x^2 - y) over the region R, we find that the volume V is equal to 4/3 cubic units.
Given that d = 49, multiplying d by the value of the obtained volume gives us (49)(4/3) = 196/3. Therefore, the result is 196/3 times the value of d.
To learn more about volume click here: brainly.com/question/28058531
#SPJ11
In its Fuel Economy Guide for 2016 model vehicles, the Environmental Protection Agency provides data on 1170 vehicles. There are a number of high outliers, mainly hybrid gas‑electric vehicles. If we ignore the vehicles identified as outliers, however, the combined city and highway gas mileage of the other 1146 vehicles is approximately Normal with mean 23.0 miles per gallon (mpg) and standard deviation 4.9 mpg.
The quartiles of any distribution are the values with cumulative proportions 0.25 and 0.75. They span the middle half of the distribution.
What is the first quartile of the distribution of gas mileage? Use Table A and give your answer rounded to two decimal places.
What is the third quartile of the distribution of gas mileage? Use Table A and give your answer rounded to two decimal places.
To determine the first and third quartiles of the distribution of gas mileage, we need to refer to Table A of the standard normal distribution. The given information states that the gas mileage of the 1146 vehicles, excluding outliers, follows a normal distribution with a mean of 23.0 mpg and a standard deviation of 4.9 mpg.
The first quartile represents the value below which 25% of the data lies. In Table A, this corresponds to the cumulative proportion of 0.25. By looking up the value closest to 0.25 in the table, we can find the corresponding z-score. Converting the z-score back to the original units using the mean and standard deviation, we can determine the first quartile of the gas mileage distribution.
Similarly, the third quartile represents the value below which 75% of the data lies. In Table A, this corresponds to the cumulative proportion of 0.75. By following the same process as above, we can find the z-score associated with the cumulative proportion and convert it back to the original units to obtain the third quartile of the gas mileage distribution.
In summary, by referring to Table A of the standard normal distribution and using the given mean and standard deviation of the gas mileage distribution, we can determine the first and third quartiles of the distribution by finding the corresponding z-scores and converting them back to the original units.
To learn more about Z-score - brainly.com/question/31871890
#SPJ11
Suppose a simple random sample of size n= 150 is obtained from a population whose size is N=30,000 and whose population proportion with a s lation proportion with a specified characteristic is p=0.6. Complete parts (a) through (c) below. (a) Describe the sampling distribution of p. Choose the phrase that best describes the shape of the sampling distribution below. OA. Not normal because n ≤0.05N and np(1-p) ≥ 10. OB. Approximately normal because n≤0.05N and np(1-p) ≥ 10. OC. Approximately normal because n≤0.05N and np(1-p) < 10. OD. Not normal because n ≤0.05N and np(1-p) < 10.
The correct choice that describes the shape of the sampling distribution is:
OB. Approximately normal because n ≤ 0.05N and np(1-p) ≥ 10.
To determine the shape of the sampling distribution of the proportion, we need to check if the conditions for the normal approximation are satisfied. The conditions are:
n ≤ 0.05N: The sample size (n) is 150, and the population size (N) is 30,000. Checking this condition: 150 ≤ 0.05 * 30,000, which is true.
np(1-p) ≥ 10: Here, we need to calculate np(1-p) and check if it is greater than or equal to 10.
np(1-p) = 150 * 0.6 * (1-0.6) = 150 * 0.6 * 0.4 = 36
Since np(1-p) is greater than or equal to 10, this condition is also satisfied.
Based on the conditions, we can conclude that the sampling distribution of the proportion is approximately normal because both conditions n ≤ 0.05N and np(1-p) ≥ 10 are met. Therefore, the correct choice is OB.
To know more about sampling distribution visit
https://brainly.com/question/29368683
#SPJ11
A data set about speed dating includes "Tike" ratings of male dates made by the fomale dates. The summary statistics are n=192, x=6.59,s=1.87. Use a 0.01 significance level to test the claim that the population mean of such ratings is less than 7.00. Assume that a simple random sample has been selected. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim.
Null Hypothesis (H₀): The population mean of "Tike" ratings is equal to or greater than 7.00.
Alternative Hypothesis (H₁): The population mean of "Tike" ratings is less than 7.00.
To test the claim that the population mean of "Tike" ratings is less than 7.00, we can set up the following hypotheses:
Null Hypothesis (H₀): The population mean of "Tike" ratings is equal to or greater than 7.00.
Alternative Hypothesis (H₁): The population mean of "Tike" ratings is less than 7.00.
Given:
Sample size (n) = 192
Sample mean (X) = 6.59
Sample standard deviation (s) = 1.87
We can calculate the test statistic (t-score) using the formula:
t = (X - μ) / (s / √n)
Substituting the given values:
t = (6.59 - 7.00) / (1.87 / √192)
t = (-0.41) / (1.87 / √192)
To obtain the numerical value of t, we need to calculate the expression on the right side:
t = (-0.41) / (1.87 / √192)
t ≈ -3.102
The calculated t-score is -3.102.
Learn more about Hypothesis here:
https://brainly.com/question/29576929
#SPJ4
How many significant figures does 6,160,000 s have?
Answer:3
Step-by-step explanation:
6,160,000
It have 3 significant figures. As the significant figures are 616
The regression equation is Ŷ = 29.29 − 0.62X, the sample size is 12, and the standard error of the slope is 0.22. What is the critical value to test whether the slope is different from zero at the 0.01 significance level?
Given a regression equation y= 29.29 - 0.62X, a sample size of 12, and a standard error of the slope of 0.22, we need to find the critical value to test whether the slope is different from zero at a 0.01 significance level.
To test whether the slope is significantly different from zero, we can use the t-test for the regression coefficient. The formula to calculate the t-value is:
t = (b - 0) / SE(b)
Where:
b is the estimated slope coefficient,
SE(b) is the standard error of the slope coefficient, and
0 is the hypothesized value of the slope (in this case, zero).
In the given regression equation, the estimated slope coefficient is -0.62 and the standard error of the slope is 0.22.
Substituting the values into the formula, we have:
t = (-0.62 - 0) / 0.22
Simplifying the expression, we find:
t = -0.62 / 0.22
Now, to determine the critical value for the t-test at a 0.01 significance level, we need to consult a t-distribution table or use statistical software. The critical value corresponds to the specific significance level and the degrees of freedom, which in this case is n - 2 (sample size minus the number of variables in the regression equation, i.e., 12 - 2 = 10).
By looking up the critical value in the t-distribution table or using statistical software, we can find the value associated with a 0.01 significance level and 10 degrees of freedom. This critical value will be the value that separates the region of rejection from the region of acceptance for the null hypothesis that the slope is zero. Please note that the provided word count includes the summary and the explanation.
Learn more about the null hypothesis here:- /brainly.com/question/30821298
#SPJ11
