P-values means in this problem is that to reject a null hypothesis it should be smaller . If p-value is large , means the alternate hypothesis is weak, so you do not reject the null.
In statistics, the p-value is the probability of obtaining results at least as extreme as the observed results of a statistical hypothesis test, assuming that the null hypothesis is correct.
The p-value serves as an alternative to rejection points to provide the smallest level of significance at which the null hypothesis would be rejected.
A smaller p-value means that there is stronger evidence in favor of the alternative hypothesis .The p-value approach to hypothesis testing uses the calculated probability to determine whether there is evidence to reject the null hypothesis.
According to the question,
If h₀ ( null hypothesis ) is true then there is a chance equal to the p-value that the average number of hours women work each week is 83 hours
It means if our p-value is bigger that it couldn't get any evidence to reject null hypothesis But if h₁ (alternative hypothesis ) is true then there is chance to the p-value that the average number of hours women work is not more 83 hours or more means the to p-value is smaller and stronger to reject null hypothesis.
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50 people were asked if they like tea, coffee and hot chocolate.
Every person liked at least one of the drinks.
17 of the people like all three drinks.
31 of the people like hot chocolate
34 of the people like tea.
21 of the people like tea and coffee.
7 of the people like tea and hot chocolate but not coffee
2 of the people like coffee and hot chocolate but not tea
Two of the 50 people are chosen at random.
Work out the probability that they both like coffee
The probability that they both like coffee is 0.405
How is the probability calculated?n(H∪T∪C) = 50
n(H∩T∩C) = 17
n(H) = 31
n(T) = 34
n(T∩C) = 21
n( T∩H -C)= 7
n( C∩ H- T) = 2
By applying combination property,
No. of ways of selecting 2 random people = x = [tex]50C_{2}[/tex]
No. of people liking coffee = n( C∩ H- T) +n( C∩ T- H) +n(H∩T∩C) +n(C)
=2 +4 + 17 +9
= 32
No. of ways of selecting 2 random people liking coffee from 32 = y
= 32[tex]C_{2}[/tex]
Probability of selecting 2 random people, both liking coffee = y/x
y / x = [tex]\frac{32C_{2}}{50C_{2}}[/tex]
[tex]=\frac{32*31}{50*49} \\\\=\frac{992}{2450} \\\\= 0.405(\text{ approximately })[/tex]
The probability that they both like coffee is 0.405
What is probability?The possibility of any random event's outcome is referred to as probability. To determine the likelihood that any event will occur is the meaning of this term. A measure of how likely something is to happen is called a probability. It gauges how likely the occurrence is to occur and aids in the clear and intelligible representation of difficult data. Chance plays a huge role in probability. Statistical methods, on the other hand, are more concerned with how we manage different types of data. The terms "dependent" and "independent" are used to describe two events where the likelihood of one event occurring has no bearing on the likelihood of the other.To learn more about probability , refer:
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Find the value of "k" that makes this a true statement:
5x+1
x-2
4x²+kx+9
x2_5+6
1
x+6
x-3
=
Answer:
there fore kx = -13x^2-73x+5
then k = -13x^2-73x+5/x
Step-by-step explanation:
given that
5x+1x-2+4x^2+kx+9x^2-5+61x+6x-3 =
= you can write it as
4x^2+9x^2+kx+6x+61x+6x-5
= 13x^2+kx+73x-5
then find kx
-kx = 13x^2+73x-5
there fore
kx = -13x^2-73x+5
then k = -13x^2-73x+5/x
What is the solution to this system of linear equations x − 3y − 2 x 3y 16?.
The solution for this system of linear equation is (-16, -5 1/3).
What is Linear equation?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
It is preferable to employ substitution while trying to solve this system of linear equations.
The first equation yields x = 3y.
In the second equation, change the value of x to be represented by the expression on the right.
-2(3y) + 3y = 16
Calculating the value of y yields;
y = -5 1/3
Solving for x with this value of y results in;
x = -16
The solution for this system of linear equation is (-16, -5 1/3).
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In a poll to estimate presidential popularity, each person in a random sample of 1,030 voters was asked to agree with one of the following statements: 1. The president is doing a good job. 2. The president is doing a poor job. 3. I have no opinion. A total of 525 respondents selected the first statement, indicating they thought the president was doing a good job.
a. Construct a 90% confidence interval for the proportion of respondents who feel the president is doing a good job. (Use z Distribution Table.) (Round your answers to 3 decimal places.) Confidence interval for the proportion is up to .
b. Based on your interval in part (a), is it reasonable to conclude that a majority of the population believes the president is doing a good job?
No Yes
The confidence interval for the proportion of respondents who feel the president is doing a good job is 48.40% < p < 53.53%
It is given that,
sample size, n = 1030
The number of people who think that the president is doing a good job, x = 525
The sample Proportion = x/n = 525/ 1030
= 0.509709
now using,
SE = sqrt [p × (1 - p) / (n)]
= sqrt [ (0.5097 × ( 1 - 0.5097)) / 1030]
= 0.015576
Z- critical for a 90% confidence interval for the proportion of respondents = 1.645 (using z Distribution Table)
thus, the lower bound = 0.509709 - 1.645 (0.015576) = 0.484085 that is 48.40%
and upper bound = 0.509709 + 1.645 (0.015576) = 0.535332 that is 53.53%
The confidence interval is 48.40% < p < 53.53%.
b. yes, a majority (53.53%) of the population believes the president is doing a good job.
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which expression is equivalent to 5x-2
Answer:B
Step-by-step explanation: Reducing 2x-2+3x results in 5x-2 because 2x+3x is 5x
Answer:
B)
Step-by-step explanation:
The answer is option B)
2x - 2 + 3x = 5x - 2
the actual voltages of power packs labeled as 12 volts for a sample are as follows: 11.17, 11.32, 11.97, 11.54, 11.77, 11.29, 11.45, 11.64. determine a point estimate of the population mean. (round your answer to 2 decimal places.)
The point estimate of the population mean is 11.51.
Explain the term population mean?A population is the entire set of people in a group, whether that group is a country or a collection of people who share a certain trait.
A population is the group of people of whom a statistical sample is taken in statistics.The average calculated from the entire community, range, or population is known as the population mean. It is calculated by dividing the sum of all population variables by both the total population of variables. The population mean is shown here as. The population's observations are summed together to form ∑X.For the data given ;
11.17, 11.32, 11.97, 11.54, 11.77, 11.29, 11.45, 11.64
Let X0 be the population mean.
Then,
X0 = ∑X / n
∑X = summation of all data
n = total number of observations.
X0 = 11.17 + 11.32 + 11.97 + 11.54 + 11.77 + 11.29 + 11.45 + 11.64 / 8
X0 = 92.15/8
X0 = 11.51
Thus, a point estimate of the population mean is 11.51.
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each marble bag sold by alonzo's marble company contains orange marbles for every blue marbles. if a bag has orange marbles, how many blue marbles does it contain?
Using the cross-multiplication method we know that the bag will contain 75 blue marbles if there will be 45 orange marbles.
What is the cross-multiplication method?When using the cross-multiplication approach, the denominator of the first term is multiplied by the numerator of the second term and vice versa.
We multiply the denominator of one side by the numerator of the other side, starting with the numerator of the first side.
So, a number of blue marbles when there are 45 orange marbles:
We know that there are 5 blue marbles when there are 3 orange marbles.
Now, we have 45 orange marbles, so the number of blue marbles will be:
The equation will be:
3/5 = 45/x
Solve the equation using the cross-multiplication method as follows:
3/5 = 45/x
3x = 5(45)
3x = 225
x = 225/3
x = 75
Therefore, using the cross-multiplication method we know that the bag will contain 75 blue marbles if there will be 45 orange marbles.
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Complete question:
Each marble bag sold by Alonzo's marble company contains 3 orange marbles for every 5 blue marble. if a bag has 45 orange marbles, how many blue marbles does it contain?
When a pre-image is dilated is the resulting image congruent to the original?.
The statement of pre-image is dilated is the resulting image congruent to the origina is false.
Explain dilation.A dilation is a change that creates a picture that is a similar shape as the first, however is an alternate size. • An expansion that makes a bigger picture is called a development. • An expansion that makes a more modest picture is known as a decrease.
According to question:As we all know that dilation is used to resize the object. It make the objects larger or smaller.
It produces an image that is the same shape as the original, but is a different size.
This means, the original figure and the transformed figure would not be congruent.
Therefore, the statement 'When an object is dilated, the resulting image is congruent to the pre-image.' is False
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Lucky's Market wanted to see if they could increase the number of sales per day before they close their locations nation wide. To test this, they randomly chose half of their 80 locations and send 50% off coupons to their customers only at those locations, while the other half of locations did not receive the 50% off coupons. They also collected information the amount of money spend on these extra customers. Which of these answers would be the best way to randomization in this study? allow location managers to volunteer O have an unbiased person just pick half of the locations for the coupons. use a computer program to select the locations who get coupons and those that don't
Correct option is:
Use a computer program to select the locations who get coupons and those who don't.
What is Volunteer role?
Volunteer work involves people giving freely of their time, labour, and skill; they frequently complete tasks that organizations would otherwise have to pay for. Governors are one example of a voluntary position in education, Trustees.
Given: Lucky's Market wanted to see if they could increase the number of sales per day before they close their locations nation wide.
To test this, they randomly chose half of their 80 locations and send 50% off coupons to their customers only at those locations, while the other half of locations did not receive the 50% off coupons.
They also collected information the amount of money spend on these extra customers.
So, the correct option is, use a computer program to select the locations who get coupons and those that don't.
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Assume that the risk-free rate of interest is 6% and the expected rate of return on the market is 11%. i am buying a firm with an expected perpetual cash flow of $1,000 but am unsure of its risk. if i think the beta of the firm is 1.1, when in fact the beta is really 2.2, how much more will i offer for the firm than it is truly worth?
i will offer $2,813.3 more for the firm than it is truly worth. if the risk-free rate of interest is 6% and the expected rate of return on the market is 11% with an expected perpetual cash flow of $1,000.
it can be calculate as follows:
Risk-free return (Rf) = 6%
Market return (Rm) = 11%
beta 1 = 1.1
Actual Beta (B2) = 2.2
capital cost Kc =Rf + B1 (Rm-Rf)
Capital cost using estimated beta = 6 + 1.1 (11 - 6) = 11.5 %
Capital cost using actual beta = 6 + 2.2 (11- 6) = 17 %
Cash flows are received till perpetuity $1000
Valuation of the firm = cash flow
cost of capital
Valuation at 11.5% cost of capital = 1000 = approximately $8,695.65
0.115
Valuation at 17% cost of capital = 1000 = approximately $5,882.35
0.17
Excess value over true value delivered = $8,695.65 - $5,882.35= $2,813.3
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Solve the equation. Remember to check for extraneous solutions.
x-5/x+5=6/x+5 +5
⇒The first step is to eliminate the fraction by multiplying all the terms with the lowest common denominator.
⇒In this case the lowest common denominator is (x+5), meaning all the terms will be multiplied by (x+5)
⇒[tex]\frac{x-5}{x+5} (x+5)=\frac{6}{x+5} (x+5)+5(x+5)[/tex]
⇒Multiply out the brackets.
[tex]x-5=6+5(x)+5(5)\\x-5=6+5x+25[/tex]
⇒Group the like terms together and simplify.
[tex]x-5x=6+25+5\\-4x=36\\\frac{-4x}{-4} =\frac{36}{-4} \\x=-9[/tex]
⇒∴ x=-9
failing to reject a false null hypothesis is classified as a a) type i error b) type ii error c) power
The answer to the given question is Type II Error.
What is Type II Error?Type II Error is a statistical term which used in the context of hypothesis testing which defines the error that happens when one fails to reject a null hypothesis which is actually false. A Type II Error constructs a false negative, and also known as an error of omission.
Type II Error is mostly caused by the statistical power of a test being low. A Type II Error will happen if the statistical test is not powerful enough. The size of the sample may also lead to a Type I Error because the outcome of the test will be afflicted.
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Graph the function below by moving the vertical asymptotes and the x intercept to the correct location, then make sure the end behavior of the function is correct. f(x) = x+2/(x + 4) (x + 1)
For given function f(x) = x+2/(x + 4) (x + 1), the graph of function is as shown below and the end behaviour of function is as x → -∞, f(x)→0, as x → +∞, f(x)→0
In this question, we have been given a function f(x) = x+2/(x + 4) (x + 1)
We need to gaph the given function.
From given function we can observe that the function f(x) is not defined for x = -4 and x = -1
Also, the degree of numerator = 1 and the degree of denominator is 2
We know that if the degree of the denominator > degree of the numerator, then a horizontal asymptote is at y = 0 (x - axis)
The graph of function f(x) is as shown below.
The x-intercept for the graph function f(x) is at (-2, 0)
Also, as x → -∞, f(x)→0
and as x → +∞, f(x)→0
Therefore, for given function f(x) = x+2/(x + 4) (x + 1), the graph of function is as shown below and the end behaviour of function is as x → -∞, f(x)→0, as x → +∞, f(x)→0
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several properties are used to evaluate this expression. identify the property used in each step. 21 (36 0 19) 21 (36 19): 21 (19 36): (21 19) 36: 40 36 76
Properties used to evaluate the expressions,
21 ( 36 0 19 ) : 21 (36 19) - Identity property21 (36 19) : 21 (19 36) - Commutative property21 (19 36) : (21 19) 36 - Associative property(21 19) 36 : 40 36 76 - Closure PropertyAddition is the basic arithmetic operation in maths. In addition, we add the integers. There are few properties of addition to add the given integers.
Additive identity property of Addition:A + 0 = 0 + A = A
⇒ 21 ( 36 + 0 + 19 ) = 21 ( 36 + 19 )
Commutative property of Addition:A + B = B + A
⇒ 21 ( 36 + 19 ) = 21 + ( 19 + 36 )
Associative property of Addition:A + ( B + C ) = ( A + B ) + C
⇒ 21 + ( 19 + 36 ) = ( 21 + 19 ) + 36
⇒ ( 21 + 19 ) + 36 = 40 + 36
Closure property of Addition:A + B = C
⇒ 40 + 36 = 76
⇒ 21 + ( 36 + 0 + 19 ) = 76
Therefore, 21 ( 36 0 19 ) : 21 (36 19) uses Identity property, 21 (36 19) : 21 (19 36) uses Commutative property, 21 (19 36) : (21 19) 36 uses Associative property and (21 19) 36 : 40 36 76 uses Closure Property.
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help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The number of students in 2001 is 150.4 thousand and the number of students in 2018 is 467.5 thousand
The number of students in 2001The function in the question is given as
y = 123.1(1.069)ˣ
Where
x is the number of years from 1998 through 2013
So, the value of x in 2001 is
x = 2001 - 1998
Evaluate
x = 3
Substitute x = 3 in the equation y = 123.1(1.069)ˣ
y = 123.1(1.069)³
Evaluate
y = 150.4
The number of students in 2018In the year 2018, the value of x is calculated as
x = Current year - 1998
So, we have
x = 2018 - 1998
Evaluate
x = 20
Substitute x = 20 in the equation y = 123.1(1.069)ˣ
y = 123.1(1.069)²⁰
Evaluate
y = 467.5
Hence, the number of students in 2018 is 467.5
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What is the scale factor used when going from the larger rectangle to the smaller one?.
Use the scaling factor equation: greater length over smaller length to go from a smaller to a larger figure. Use the formula scale factor = smaller length over larger length if you're scaling down from a larger to a smaller figure.
What is scale factor in math?
The ratio of one object's scale to that of a new object, which has its representation but is larger, is known as a scale factor (bigger or smaller). By multiplying each side by a certain number, say 2, we can increase the size of a rectangle with sides of 2 cm and 4 cm.How can I calculate the scale factor?
The scale factor is calculated using the following fundamental formula Scale factor = Dimension of the new shape Dimension of the old shape. The formula for calculating the scale factor is written as Scale factor = Larger figure dimensions Smaller figure dimensions in the event that the original figure is magnified.Learn more about scale factor
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a number,h, rounded to 2sf is 0.072 what is the error interval
Answer:
Step-by-step explanation:
What is 2sf?
HELP QUICKLYYYYY PLEASEEEEEE
Answer:
slope =- [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (2, - 3 ) and (x₂, y₂ ) = (5, - 4 )
m = [tex]\frac{-4-(-3)}{5-2}[/tex] = [tex]\frac{-4+3}{3}[/tex] = [tex]\frac{-1}{3}[/tex] = - [tex]\frac{1}{3}[/tex]
Answer:
points are ;
(2,-3).......X1,Y(5,-4).......X2, Y2
now
slope(m)=y2 -Y1 / X2-X1
= -4+3 / 5-2
-1 / 3
How to do this
Help project do tomorrow
The number of tables and chairs will the school purchase for the cafeteria exists tables and chairs will the school purchase for the cafeteria exists 10 tables and 80 chairs.
What is meant by mathematical operation?A function that converts zero or more input values into a clearly defined output value is referred to in mathematics as an operation. The operation's complexity is measured by the number of operands.
A value is computed utilizing operands and a math operator as part of the mathematical "operation." In order to be applied to the provided operands or integers, the math operator's symbol has predetermined rules.
In each table, there are 8 chairs. 8 × 40 = 320
1 table cost 200$
Each set of table + chairs is 200 + 320 = 520
Total amount of money the school can spend is 5200
Therefore 5200 ÷ 520 = 10
So there are 10 sets of Table + chairs
So there are 10 tables
Total amount of chairs is 8 × 10 = 80
Therefore, the number of tables and chairs will the school purchase for the cafeteria exists tables and chairs will the school purchase for the cafeteria exists 10 tables and 80 chairs.
The complete question is:
To furnish a school cafeteria a school can spend $5200 on tables and chairs. Tables cost $200 each and chairs cost $40. There are 8 times as many chairs as tables. How many tables and chairs will the school purchase for the cafeteria?
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Is every linear equation a quadratic equation?.
No, every linear equation is not a quadratic equation.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
Any equation of the form ax²+bx+c=0 where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
Every linear equation is also a quadratic equation. A polynomial equation is a linear equation or a quadratic equation.
Thus, not every linear equation is not a quadratic equation.
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The world record for the most number of speed skips in 60 seconds is 332 skips. If the record holder skipped at a constant ratio of seconds to skips, how many skips did she make in 15 seconds?
How do you find the equation of a line that is perpendicular and passing through a point?.
The equation of a line that is perpendicular and passing through a point is y = -1/m + (y1 + x1/m).
Let y = mx + b be the perpendicular line and (x1,y1) be the point.
slope of y = mx + b is:
= m
we know that,
perpendicular slope = -1/m
substitute m and (x1,y1)
y1 = -1/m(x1) + b
y1 + x1/m = b
substitute b value in y = -1/m + b.
y = -1/m + (y1+x1/m)
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What is HCF and LCM of 14 and 28?.
The HCF and LCM of 14 and 28 are 14 and 28 respectively.
Highest Common Factor:
The full form of HCF in maths is the Highest Common Factor. HCF of two or more numbers is the greatest factor that divides the numbers. For example, 2 is the HCF of 4 and 6.
Lowest common multiple:
LCM stands for least common multiple. The least common multiple of two numbers is the smallest number which is a multiple of both of them.
Here we have to find the HCF and LCM of 14 and 28.
The two numbers are 14 and 28.
We can write the number as:
14 = 2 × 7
28 = 2² × 7
The HCF is the common number in both the number, which is 2 and 7.
So HCF of two number = is 2 × 7
= 14
The LCM is the largest common multiple of the given numbers.
So LCM of two number = is 2² × 7
= 28
Therefore the HCF and LCM are 14 and 28 respectively.
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calculate length of AC
Answer:
[tex] \sqrt{ {12}^{2} + {9}^{2} } \\ = \sqrt{144 + 81} \\ = \sqrt{225} \\ = 15cm[/tex]
Step-by-step explanation:
AB²+ BC²= AC²
AC= √AB²+BC²
Is 30% of a number is 12. 6 find the number?.
Screen, teen, and pychological well-being. In a tudy of three nationally repreentative largecale data et from Ireland, the United State, and the United Kingdom (n ), teenager between the age of 12 to 15 were aked to keep a diary of their creen time and anwer quetion about how they felt or acted. The anwer to thee quetion were then ued to compute a pychological well-being core. Additional data were collected and included in the analyi, uch a each child' ex and age, and on the mother' education, ethnicity, pychological ditre, and employment. The tudy concluded that there i little clear-cut evidence that creen time decreae adolecent well-being. (a) What type of tudy i thi?
(b) Identify the explanatory variable. (c) Identify the repone variable. (d) Comment on whether the reult of the tudy can be generalized to the population, and why. (e) Comment on whether the reult of the tudy can be ued to etablih caual relationhip
A. What type of study is this?
ANSWER: An observational study
B. Identify the explanatory variables.
ANSWER: Screen time
C. Identify the response variable.
ANSWER: Adolescent well-being
D. Comment on whether the results of the study can be generalized to the population, and why.
ANSWER: It cannot as there was no control group and even though it states that these populations are nationally representative of these nations there is not quite enough information to prove that. There also seems to be no randomization.
E. Comment on whether the results of the study can be used to establish causal relationships.
ANSWER: No, there is too many lurking variables in an observational study to establish causation.
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Which of the following are the recommended percentage groupings of the ABC classifications of the dollar volume of products?A items get 25%, B items get 15%, and C items get 60%A items get 15%, B items get 45%, and C items get 40%A items get 25%, B items get 35%, and C items get 40%A items get 10%, B items get 40%, and C items get 50%A items get 20%, B items get 30%, and C items get 50%
Recommended percentage grouping of ABC classification is A items get 20%, B items get 30% and C items get 50%.
What is Dollar volume?
DOLLAR VOLUME is the result of multiplying the closing price by the principal market's trading volume on a given trading day.
DOLLAR VOLUME refers to the dollar volume of shares of Common Stock traded on the Principal Market on a Trading Day for any given Trading Day.
When referring to residential real estate, the term "dollar volume" simply refers to the sum of all residences' sales prices during a specific time period (month, quarter, year). It does not divide out by unit count like average sales price, but rather represents the largest dollar-based measure of sales activity.
Hence, Recommended percentage grouping of ABC classification is A items get 20%, B items get 30% and C items get 50%.
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The following cross-tabulation shows the number of people who rated a customer service representative as friendly and polite based on whether the representative greeted them first. a. Write the hypotheses for the chi-square test for independence. b. Find the expected frequencies. C. Compute the chi-square statisticising a level of significance of 0.01. d. Find the chi-square critical value and p-value and draw a conclusion.
The hypotheses for the chi-square test for independence is:
The null hypothesis holds that staff friendliness and greetings are unrelated. Ha, the other view holds that staff friendliness and greetings are interdependent.
Define hypothesis.A hypothesis is a statement that makes sense in light of the available information but hasn't been proved true or wrong. A hypothesis in statistics is a claim that will serve as the foundation for hypothesis testing (also known as a statistical hypothesis). A hypothesis in mathematics is an unproven claim that is backed up by all the information that is known as well as numerous weaker findings.
Given,
Cross-tabulation shows the number of people who rated a customer service representative as friendly and polite based on whether the representative greeted them first.
Hypothesis for the chi-square test for independence,
The null hypothesis holds that staff friendliness and greetings are unrelated.
Ha, the other view holds that staff friendliness and greetings are interdependent.
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Medical School Applications A medical college dean read that the average number of applications a potential medical school student sends is 7.8. She thinks that the mean is higher. So she selects a random sample of 35 applicants and asks each how many medical schools they applied to. The mean of the sample is 8.7. The population standard deviation is 2.6. Test her claim at α 0.01
A Sample of medical students Applications in a medical College .
To check the claim of college Dean is correct or not we will use hypothesis testing with Z-test.
H₀ : μ = 7.8
= 7.8 Hₐ : μ > 7.8
There we see fail to reject the null hypothesis.
So, her claim that mean in higher is right.
We have given that,
Medical school applications of students in a medical College is a sample .
Sample size, n = 35
Mean of sample , X-bar = 8.7
population standard deviations, σ = 2.6
significance level, α = 0.01
Consider null and alternative hypothesis to test:
H₀ : μ = 7.8
Hₐ : μ > 7.8
Test Statistic (Z-score) :
Z = ( X-bar - μ ) / σ / √n
Z = ( 8.7 - 7.8 ) / ( 2.6 /sqrt(35 ))
Z = 2.0479 ~ 2.05
Test Criteria :-
We can reject null hypothesis if Z > Zₐ
Zₐ = Z₀.₀₁ = 2.33
that is 2.33 > 2.05 or Zₐ> Z
Thus, fail to reject null hypothesis .
There is insufficient evidence to support the claim that mean is higher.
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Directed line egment ¯¯¯¯¯¯ A B ha endpoint A ( − 8 , 7 ) and B ( 7 , − 3 ) What are the coordinate of P uch that P i the point partitioning ¯¯¯¯¯¯ A B in the ratio 1 : 4 ? Write each coordinate a a implified fraction if neceary
The coordinate of point P is (-5,5).
It is given that AB has endpoint A(-8,7) and B(7,-3) also P is the point partitioning AB in the ratio 1:4.
We have to find the coordinates of P.
So distance in x-coordinate between A and B is,
ABx = 7 - (-8) = 15 units
distance in y-coordinates between A and B is,
ABy = -3 - 7 = -10 units
Now the point P partitioning AB in the ratio 1:4
i.e [tex]\frac{AP}{AB}[/tex] = [tex]\frac{1}{1+4}[/tex]
[tex]\frac{AP}{AB}[/tex] = [tex]\frac{1}{5}[/tex]
we will find x-coordinate of point P
⇒ [tex]\frac{APx}{ABx}[/tex] = [tex]\frac{1}{5}[/tex]
⇒ [tex]\frac{APx}{15}[/tex] = [tex]\frac{1}{5}[/tex]
⇒ APx = 3
Therefore the x-coordinates of P is
Px = Ax + APx
⇒ Px = -8 + 3 = - 5
And y-coordinate of pint P is,
[tex]\frac{APy}{ABy}[/tex] = [tex]\frac{1}{5}[/tex]
[tex]\frac{APy}{-10}[/tex] = [tex]\frac{1}{5}[/tex]
APy = -2
i.e Py = APy + Ay
= -2 + 7
Py = 5
Therefore the coordinate of point y is (-5,5).
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