when to use the one mean z test for large samples (size 30 or more)
We should use the one mean z-test for large samples (size 30 or more) when dealing with quantitative data, the sample size is at least 30, and the population standard deviation is known.
When to use the one mean z-test for large samples (size 30 or more).
we should use the one mean z-test for large samples in the following situations:
Sample size (n) is greater than or equal to 30:
The one mean z-test is appropriate for large samples, typically when the sample size is 30 or more.
This is because the Central Limit Theorem states that for a sufficiently large sample size, the sampling distribution of the mean is approximately normally distributed.
Population standard deviation (σ) is known:
The one mean z-test requires knowledge of the population standard deviation.
If the population standard deviation is unknown, you should use the t-test instead.
The variable of interest is quantitative:
The one mean z-test is designed for quantitative data (interval or ratio scale).
If you are dealing with categorical or ordinal data, would need to use different tests, such as the chi-square test or Mann-Whitney U test.
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Using the definitions of sine and cosine on a right triangle, explain why each point (x, y) on the unit circle can be written as (cosθ, sinθ).
Any point on the unit circle may be expressed as (cos, sin), which denotes the angle formed between the radius of the point and the positive x-axis.
In a right triangle, the sine of an angle is defined as the length of the side opposite the angle divided by the length of the hypotenuse, and the cosine of an angle is defined as the length of the adjacent side divided by the length of the hypotenuse.
By definition, the cosine of θ is x (the length of the adjacent side) divided by 1 (the length of the hypotenuse), or simply x/1, which is just x. Similarly, the sine of θ is y (the length of the opposite side) divided by 1 (the length of the hypotenuse), or simply y/1, which is just y.
So we have shown that, for any point (x, y) on the unit circle, the cosine of the angle θ between the positive x-axis and the radius to the point is equal to x, and the sine of θ is equal to y.
Therefore, we can write any point on the unit circle as (cosθ, sinθ), where θ is the angle between the positive x-axis and the radius of the point.
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A student would like to estimate the proportion of students at his school who have lunch during period 4. To do so, he selects a random sample of 40 students and finds that 30% of them have period 4 lunch. Later he goes to the guidance office and finds that of the 380 students at this school 25% of them have period 4 lunch. Which of the following properly describes the number 25%?
A. Sample
B. Statistic
C. Population
D. Parameter
The number 25% represents the proportion of the entire population of students at the school who have period 4 lunch. Therefore, it is a option D- parameter.
A statistic is a numerical summary of a sample, while a parameter is a numerical summary of a population. In this case, the proportion of students who have period 4 lunch in the sample of 40 students is 30%, which is a statistic. The proportion of students who have period 4 lunch in the entire population of 380 students is 25%, which is a parameter.
It's important to distinguish between a sample and a population because statistical conclusions drawn from a sample cannot be automatically generalized to the population from which the sample was drawn. In other words, the characteristics of a sample may not perfectly reflect the characteristics of the larger population, due to random sampling variation. Therefore, when making statistical inferences or drawing conclusions about a population, it's important to use appropriate sampling methods and to carefully consider the limitations and assumptions of statistical analyses.
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Which diagram shows how Eliza should cut the parallelogram?
Answer:
A
Step-by-step explanation:
PLAto
<ABC has a measure of 40° and <CBD <CBD has q
measure of 23:. the angles share a rau and Form <ABD
write and solve an equation to find the measure of
<ABD.
After analysing the given data we conclude that the measure of <ABD is 117 degrees, under the condition that <ABC has a measure of 40°.
Now in order to evaluate the angle we have to relie on the principles of angle to derive a formula
The formula is
180 - ( remaining angles) = ( unknown angle)
Now, to find the measure of <ABD, we can apply the fact that the sum of the angles in a triangle is 180 degrees. It is known that <ABC has a measure of 40 degrees and <CBD has a measure of 23 degrees. Since <ABC and <CBD share a ray, we can add their measures to get the measure of <ABD.
Placing the values in the formula
Therefore,
<ABD = 180 - 40 - 23
= 117 degrees.
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Imagine folding a piece of paper in half, again and again. What is the relationship between the number of folds and the area
of the top piece of paper? Imagine starting out with a sheet of paper that is 10 inches long and 8 inches wide. Work
through the following questions to investigate this relationship.
1. What is the area of the original piece of paper?
What is the equivalent of 1 000 mg to g
Answer:
1 gram is the equivalent of 1000 mg to g
Answer:
0,001
Step-by-step explanatio}
Joe had been saving up all of his tickets from his day at the amusement park. He used ⅗ of them on a stuffed bear for his sister. He then had 96 tickets left to use. How many tickets did Joe win at the park?
The total number of tickets that Joe win at the park is 240 if the fraction of 3/ is used.
Given that,
Joe had been saving up all of his tickets from his day at the amusement park.
Let x be the total number of tickets he saved.
He used a fraction of ⅗ of them on a stuffed bear for his sister.
x - (3/5 x) = 96
2/5 x = 96
Multiplying both sides by 5/2, we get,
x = 96 × 5/2
x = 240
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Suppose we select an SRS of size n=100 from a large population having proportion p of successes. Let p be the proportion of successes in the sample. For which value of p would it be safe to use the Normal approximation to the sampling distribution of p? a) 0.85 b) 0.975 c) 0.999 d) 0.01 e) 0.09 10
The normal approximation to the sampling distribution of a proportion can be used when both np and n(1-p) are greater than or equal to 10.
For which value of p would it be safe to use the Normal approximation to the sampling distribution of p?
In this problem, we are selecting an SRS of size n=100 from a large population with a proportion p of successes. We need to find the value of p that would make it safe.
To use the normal approximation to the sampling distribution of p.
For each given value of p, we can calculate np and n(1-p), and then determine whether both of these values are greater than or equal to 10.
a) p = 0.85
np = 85, n(1-p) = 15
Both np and n(1-p) are greater than or equal to 10, so the normal approximation is safe.
b) p = 0.975
np = 97.5, n(1-p) = 2.5
Only np is greater than or equal to 10, so the normal approximation is safe.
c) p = 0.999
np = 99.9, n(1-p) = 0.1
Only np is greater than or equal to 10, so the normal approximation is safe.
d) p = 0.01
np = 1, n(1-p) = 99
Only n(1-p) is greater than or equal to 10, so the normal approximation is safe.
e) p = 0.09
np = 9, n(1-p) = 91
Only n(1-p) is greater than or equal to 10, so the normal approximation is safe.
Therefore, for all given values of p, it is safe to use the normal approximation to the sampling distribution of p.
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(7-6i)(3+2i) what is the answer to this
Answer:
33 - 4i
Step-by-step explanation:
note that i² = - 1
(7 - 6i)(3 + 2i) ← expand using FOIL
= 21 + 14i - 18i - 12i²
= 21 - 4i - 12(- 1)
= 21 - 4i + 12 ← collect like terms
= 33 - 4i
A candy dispenser can hold 15 cups of candy the candy dispenser is 75 percent full after a few hours 8 percent of the candy has been sold how much candy in cups remains in the candy dispenser
The amount of candy remaining in the dispenser is 10.35 cups. There are 10.05 cups of candy remaining in the dispenser.
The candy dispenser can hold 15 cups of candy. If the dispenser is 75% full, then it contains 75% of 15 cups, which is:
0.75 x 15 = 11.25 cups
After a few hours, 8% of the candy has been sold. This means that 8% of 15 cups has been sold, which is:
0.08 x 15 = 1.2 cups
To find out how much candy remains in the dispenser, we need to subtract the amount sold from the amount that was initially in the dispenser. So, the amount of candy remaining in the dispenser is:
11.25 - 1.2 = 10.05 cups
Therefore, there are 10.05 cups of candy remaining in the dispenser.
Alternatively, we can calculate the amount of candy remaining in the dispenser directly as follows:
The dispenser is 75% full, which means that 25% of its capacity is empty. Therefore, the empty space in the dispenser is:
0.25 x 15 = 3.75 cups
If 8% of the candy has been sold, then 92% of the candy remains in the dispenser. Therefore, the amount of candy remaining in the dispenser is:
0.92 x (15 - 3.75) = 0.92 x 11.25 = 10.35 cups
This gives us the same answer as before, which is that there are 10.05 cups of candy remaining in the dispenser.
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HOWW? PLEASE SOMEONE EXPLAIN THIS TO ME THIS IS MEANT TO BE EASY MATHS!
Equation A: 3x + y = 6
Equation B: 6x - 2y = 4
Equation C: y = 3x - 2
Equation D: y = 13x + 7
Which two lines are perpendicular?
A) A and B
B) B and C
C) A and D
D) C and D
None of the given pairs of lines are perpendicular. The answer is none of the above (E).
To determine which two lines are perpendicular, we need to check whether the slopes of the lines are negative reciprocals of each other. If they are, then the lines are perpendicular.
The slope of a line can be determined by examining the coefficient of x in the line's equation.
For Equation A, the slope is -3 (the coefficient of x is 3, and the slope is the negative of the coefficient).
For Equation B, the slope is 3 (the coefficient of x is 6, and the slope is the coefficient divided by -2).
For Equation C, the slope is 3 (the coefficient of x is 3).
For Equation D, the slope is 13.
Now we can check which two lines have slopes that are negative reciprocals of each other. The negative reciprocal of 3 is -1/3, and the negative reciprocal of -3 is 1/3. None of the pairs of lines have slopes that are negative reciprocals of each other. Therefore, none of the given pairs of lines are perpendicular. The answer is none of the above (E).
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kimberly is making a wall hanging. she has graphed the wall hanging as polygon are A(1,5),B(1,9),C(7,9),D(7,5),E(5,3), and F(3,3). graph the polygon on the coordinate plane. Waht is the area of Kimberly's wall hanging.
The area of Kimberly's wall hanging will be 32 square units.
Given that:
Points, A(1, 5), B(1, 9), C(7, 9), D(7, 5), E(5, 3), and F(3, 3)
The area of a two-dimensional figure is the area that its perimeter encloses. The quantity of unit squares that occupy a closed figure's surface is its region.
The polygon is shown in the graph below.
The area of the polygon is given as,
A = Area of rectangle + Area of trapezium
A = 4 x 6 + 1/2 x (6 + 2) x 2
A = 24 + 8
A = 32 square units
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What is the domain of the function shown in the graph below?
Answer:
(-2, ∞)
Step-by-step explanation:
The domain of a function is how far the x goes left and right.
We see the x starts at -2 and goes forever.
So, the Domain of the function is (-2, ∞)
Write the equation in point slope form,with the given criteria
M=3 and (-4,5)
Answer:
y-5=3(x+4)
Step-by-step explanation:
point slope form: y-y1=m(x-x1)
plug in 5 for y1, -4 for x1
y-5=3(x+4)
How much money was deposited if 5800 was returned in four years at the rate of 4% simple interest per annum?
The solution is :
The sum of money deposited is approximately $22,021.74
Here, we have,
The given interest and amounts of the deposit are outlined as follows;
The simple interest per annum, R = 0.325%
The number of years the money is deposited, T = 4 years
The total amount received (Interest + Initial deposit), A = $50,650
We have;
I = P × R × T
Where;
P = The principal (initial amount deposited)
R = The (annual) interest rate = 0.325%
T = The time = 4 years
Therefore;
The total amount received, A = P + I
P + I = P + P × R × T = P × (1 + R × T)
∴ A = P + I = P × (1 + R × T)
P = A/(1 + R × T)
Plugging in the values, gives;
P = 50,650/(1 + 0.325 × 4) = 506,500/23 ≈ 22,021.74
The sum of money deposited, P = $22,021.74
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complete question:
A sum of money is deposited in a bank which offers a simple interest rate of 0.325% per annum. At
the end of the 4 years, the total amount receives is $50 650. Find the sum of money deposited.
Let f be the function given by f(x)= kx/x^2+1, where k is a constant. For what values of k, if any, is f strictly decreasing on the interval (-1, 1)?
A. k<0
B. k= 0
C. k>0
D. k>1 only
E. There are no such values of k
The answer is (A) k < 0. When k is negative, f'(x) is negative on (-1,1), which means that f(x) is strictly decreasing on (-1,1). The correct answer is option a.
To determine for what values of k the function [tex]f(x) = kx/(x^2+1)[/tex]is strictly decreasing on the interval (-1, 1), we need to find the first derivative of f(x) and then examine its sign.
We have:
[tex]f(x) = kx/(x^2+1)\\f'(x) = (k(x^2+1) - kx(2x))/(x^2+1)^2\\f'(x) = k(1-x^2)/(x^2+1)^2[/tex]
To determine when f(x) is strictly decreasing on (-1,1), we need f'(x) to be negative on that interval. Therefore, we need [tex](1-x^2)/(x^2+1)^2[/tex] to be negative on (-1,1).
Note that [tex](1-x^2)[/tex] is always non-negative on the interval (-1,1), so for f'(x) to be negative, we need [tex](x^2+1)^2[/tex] to be positive. Since [tex](x^2+1)^2[/tex] is always positive, we can conclude that f'(x) is negative on the interval (-1,1) if and only if k < 0.
Therefore, the answer is (A) k < 0. When k is negative, f'(x) is negative on (-1,1), which means that f(x) is strictly decreasing on (-1,1). When k is zero or positive, f'(x) is zero or positive on (-1,1), respectively, which means that f(x) is not strictly decreasing on (-1,1).
The correct answer is option a.
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In a random sample, 24 out of 60 households had a dog in the town of Nowaday. If the town has 3,000 households, approximately how many of the households have a dog
Answer:
We can use proportion to estimate the number of households that have a dog in the town of Nowaday.
From the data given in the random sample, we know that 24 out of 60 households had a dog. This can be written as:
24/60 = x/3000
where x is the number of households in the town that have a dog.
To solve for x, we can cross-multiply and simplify:
24 x 3000 = 60 x x
x = (24 x 3000) / 60
x = 1,200
Therefore, we can estimate that approximately 1,200 households in the town of Nowaday have a dog.
The following is a Poisson probability distribution with µ = 0.1. x P(x)
0 0.9048
1 0.0905
2 0.0045
3 0.0002
The mean of the distribution is _____.
The mean of the Poisson distribution is 0.1.
The mean of a Poisson distribution is given by µ, which is the expected number of occurrences in the specified interval. In this case, µ = 0.1, which means we expect to have 0.1 occurrences in the specified interval.
The mean can also be calculated by using the formula µ = ΣxP(x), where ΣxP(x) is the sum of the product of each value of x and its corresponding probability.
µ = (0 × 0.9048) + (1 × 0.0905) + (2 × 0.0045) + (3 × 0.0002)
µ = 0 + 0.0905 + 0.009 + 0.0006
µ = 0.1
Therefore, the mean of the Poisson distribution is 0.1.
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Question 4(Multiple Choice Worth 2 points)
(Three-Column Tables MC)
A three-column table is given.
Part A CD
Part 14 28 63
Whole 20 B 90
What is the value of B in the table?
30
034
040
055
Suppose the competing hypotheses for a test are H0: μ ≥ 10 versus Ha: μ < 10. If the value of the test statistic is -2.50 and the critical value at the 5% level of significance is -z0.05 = -1.645, what is the correct conclusion?
we can conclude that there is significant evidence to support the claim that μ is less than 10.
What is the conclusion for a test with H0: μ ≥ 10 versus Ha: μ < 10, if the test statistic is -2.50 and the critical value at 5% level is -1.645?We need to compare the test statistic with the critical value to determine whether to reject or fail to reject the null hypothesis. Since the test statistic (-2.50) is less than the critical value (-1.645), we can reject the null hypothesis at the 5% level of significance.
The conclusion is that there is sufficient evidence to support the alternative hypothesis Ha: μ < 10. This means that the sample data suggests that the true population mean is less than 10, and we can reject the possibility that the population mean is greater than or equal to 10.
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what is the symbol of the hectare a/ha?
The symbol for a hectare is "ha." A hectare is a unit of area measurement, primarily used in the field of agriculture and land management. It is equal to 10,000 square meters or approximately 2.47 acres.
The term "hectare" is derived from the metric prefix "hecto," which means one hundred, and the unit of area "are," which equals 100 square meters. Therefore, a hectare is equivalent to 100 ares (100 x 100 square meters).
The hectare is widely used in many countries around the world to describe the size of agricultural land, forests, parks, and other large areas. Its use is more common in countries that have adopted the metric system, such as in Europe and Asia. In contrast, countries like the United States often use acres as their primary unit of land measurement.
In summary, "ha" is the symbol used to represent a hectare, a unit of area measurement often utilized in agriculture and land management. It is equivalent to 10,000 square meters or about 2.47 acres and is commonly used in countries that follow the metric system.
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If you deposit $250 each much how much will you have towards the purchase of a boat after three years with an apr of 8. 4%
After three years with a monthly deposit of $250 and an APR of 8.4%, you will have approximately $10,093.46 towards the purchase of a boat.
To calculate the amount you will have towards the purchase of a boat after three years with an APR (Annual Percentage Rate) of 8.4% and monthly deposits of $250, we can use the formula for the future value of a series of regular deposits:
FV = P * [(1 + r)^n - 1] / r
Where:
FV is the future value of the deposits
P is the monthly deposit amount ($250)
r is the monthly interest rate (8.4% / 12 = 0.007)
n is the number of periods (3 years * 12 months = 36)
Let's calculate the future value:
FV = $250 * [(1 + 0.007)^36 - 1] / 0.007
FV ≈ $10,093.46
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the area of a right angled triangle below is 23.66 cm what is the size of angle y
The size of the angle y as required to be determined in the task content is; 60°.
What is the side of the angle y as required?As evident in the task content, the base of the triangle is; 9.1 cm.
Recall the area of a right triangle is; A = bh / 2
Therefore, to determine the height h given an area of 23.66 cm²; we have that;
23.66 = 9.1h / 2
h = (2 × 23.66) / 9.1
h = 5.2 cm.
Ultimately, to determine the size of y from trigonometric ratios;
tan y = 9.1 / 5.2
y = tan-¹ (9.1/5.2)
y = 60° to the nearest integer.
Ultimately, the size of the angle y as required in the task content is; 60°.
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I'm stuck on this question
Answer:
Domain: [1,3]
Range: [0.5,1.5]
Step-by-step explanation:
Domain: x-values
Range: y-values
You are getting ready to open The Shoe Hut, but you need to need to determine whether you have the absolute or comparative advantage in the production of specific items. This will help you determine which product is the best for specialization.
Your production possibilities are as follows:
• You have the resources to produce up to 15 running shoe inserts.
• You have the resources to produce up to 10 hiking boot inserts.
• For every 2 hiking boot inserts produced, you give up the production of 3 running shoe inserts.
Your production possibilities schedule will help you determine:
• your opportunity costs.
• your best options for production.
1. Using the information that you learned about your ability to produce running shoe inserts and hiking boot inserts, complete your production possibilities schedule. (5 points)
2. Use the information from your production possibilities schedule to create your production possibilities curve by filling in the following graph. Use textboxes to insert text, and use lines and circles from the shapes function to illustrate your production possibilities. Be sure to mark points A through F on the graph. (5 points)
3. Based on the data within your schedule and curve, are you using your resources efficiently? Support your answer using the data presented. (5 points)
4. Based on the information you used to create your schedule and curve, which product would you recommend the Shoe Hut focus on, and why? Provide details that support your answer. (5 points)
Tyler has 3 times as many books as Mai.
a. How many books does Mai have if Tyler has:
i.15 books?
ii. 21 books?
iii. x books?
An 8-inch diameter pizza stone costs $14.35.
Marco estimated that a 16-inch diameter pizza
stone (same thickness) should cost $28.70. Based
on the areas of the two pizza stones, is Marco's
estimate reasonable? Explain your answer. Please help! Thank you!
Answer:
No, it is not reasonable.
Step-by-step explanation:
Given an 8-inch pizza costs $14.35, you want to know if an estimated cost of $28.70 is reasonable for a 16-inch pizza.
AreaThe scale factor for area is the square of the scale factor for linear dimensions such as diameter.
The ratio of diameters is ...
(16 in)/(8 in) = 2
Then the ratio of areas will be 2² = 4. The larger pizza will have 4 times the area of the smaller one.
If cost is based on area, then a better estimate of the cost of a 16-inch pizza is ...
4 × $14.35 = $57.40
Marco's estimate of $28.70 is not reasonable. A better estimate is $57.40.
__
Additional comment
The area is given by the formula ...
A = (π/4)d²
When the diameter is doubled, the area becomes ...
A' = (π/4)(2d)² = 4×(π/4)d² = 4A
You can see that the scale factor 2 was squared when we expanded (2d)² to 2²·d² = 4d².
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Suppose x is a normally distributed random variable with µ= 50 and σ = 3. Find a value of the random variable, call it x0, such that
c) P ( x > x0 ) = 0.025
The value of the random variable x0 such that P (x > x0) = 0.025 is approximately 55.88.
To find the value of x0 such that P(x > x0) = 0.025, we need to use the standard normal distribution table or a calculator to find the corresponding z-score.
First, we need to standardize x using the formula:
z = (x - µ) / σ
where µ = 50 and σ = 3.
So,
z = (x - 50) / 3
Now, we want to find the z-score that corresponds to a probability of 0.025 in the right tail of the standard normal distribution. From the standard normal distribution table, we can see that the z-score for this probability is approximately 1.96.
Therefore,
1.96 = (x0 - 50) / 3
Multiplying both sides by 3, we get:
x0 - 50 = 1.96 * 3
x0 - 50 = 5.88
Adding 50 to both sides, we get:
x0 = 55.88
So, the value of the random variable x0 such that P(x > x0) = 0.025 is approximately 55.88.
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