Describe the shape of the sampling distribution of X ¯ if n = 4 .

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Answer 1

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Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Chapter 7, Problem 6PS

a.

To determine

Describe the shape of the sampling distribution of X¯ if n=4 .

b.

To determine

Describe the shape of the sampling distribution of X¯ if n=100 .

c.

To determine

Determine the probability that the sample mean will be less than $315,000 .

d.

To determine

Determine the probability that the sample mean will lie between $295,000 and $310,000 .

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You receive a brochure from a large university. The brochure indicates that the mean class size for full-time faculty is fewer than 31 students. You want to test this claim. You randomly select 18 classes taught by full-time faculty and determine the class size of each. The results are shown in the table below. At α = 0.05, can you support the university's claim? Complete parts (a) through (d) below. Assume the population is normally distributed. 36 28 25 27 29 35 32 39 31 28 380 22 26 29 24 27 24 30吋 24 (a) Write the claim mathematically and identify Ho and Ha. Which of the following correctly states Ho and H₂? ○ A. Ho: μ31 Нa: μ≤31 E. Ho: "=31 Ha: μ 31 OF. Ho: μ=31 Нa: μ31

Test the claim about the population mean μ at the level of significance α. Assume the population is normally distributed. μ Claim: <4715; α = 0.05 Sample statistics: x = 4917, s = 5501, n = 54 What are the null and alternative hypotheses? Ho: Ha (Type integers or decimals. Do not round.) Find the standardized test statistic t. t = ☐ (Round to two decimal places as needed.) Find the P-value. P = (Round to three decimal places as needed.) Decide whether to reject or fail to reject the null hypothesis. Choose the correct answer below. Ho. There enough evidence at the ☐ % level of significance to Fail to reject Reject .... the claim.

A politician claims that the mean salary for managers in his state is more than the national mean, $85,000. Assume the the population is normally distributed and the population standard deviation is $8700. The salaries (in dollars) for a random sample of 30 managers in the state are listed. At α = 0.01, is there enough evidence to support the claim? Use technology. 92,421 81,412 85,143 97,220 99,317 71,884 97,762 86,108 98,385 73,869 81,391 95,997 98,828 86,476 77,893 74,995 90,472 81,330 92,183 94,649 77,880 91,821 90,907 84,640 78,479 81,703 89,573 89,948 70,938 81,300 (a) Identify the null hypothesis and alternative hypothesis. O A. Ho: " =85,000 Нa: μ85,000 D. Hoi u >85,000 Нa: μ≤85,000 (b) Identify the standardized test statistic. Z= B. Hoμ≥85,000 Haμ85,000 Haμ≤85,000 (Round the final answer to two places as needed. Round all intermediate values to three places as needed.) (c) Find the P-value. Use technology. (Round to three decimal places as needed.) (d) Decide whether to reject…

Answer 2

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Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Chapter 7, Problem 6PS

a.

To determine

Describe the shape of the sampling distribution of X¯ if n=4 .

b.

To determine

Describe the shape of the sampling distribution of X¯ if n=100 .

c.

To determine

Determine the probability that the sample mean will be less than $315,000 .

d.

To determine

Determine the probability that the sample mean will lie between $295,000 and $310,000 .

Expert Solution & Answer

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Answer 3

Question

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Chapter 7, Problem 6PS

a.

To determine

Describe the shape of the sampling distribution of X¯ if n=4 .

b.

To determine

Describe the shape of the sampling distribution of X¯ if n=100 .

c.

To determine

Determine the probability that the sample mean will be less than $315,000 .

d.

To determine

Determine the probability that the sample mean will lie between $295,000 and $310,000 .

Expert Solution & Answer

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Answer 4

Question

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Chapter 7, Problem 6PS

a.

To determine

Describe the shape of the sampling distribution of X¯ if n=4 .

b.

To determine

Describe the shape of the sampling distribution of X¯ if n=100 .

c.

To determine

Determine the probability that the sample mean will be less than $315,000 .

d.

To determine

Determine the probability that the sample mean will lie between $295,000 and $310,000 .

Expert Solution & Answer

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Answer 5

Chapter 7, Problem 6PS

a.

To determine

Describe the shape of the sampling distribution of X¯ if n=4 .

b.

To determine

Describe the shape of the sampling distribution of X¯ if n=100 .

c.

To determine

Determine the probability that the sample mean will be less than $315,000 .

d.

To determine

Determine the probability that the sample mean will lie between $295,000 and $310,000 .

Answer 6

Chapter 7, Problem 6PS

a.

To determine

Describe the shape of the sampling distribution of X¯ if n=4 .

Answer 7

Chapter 7, Problem 6PS

a.

To determine

Describe the shape of the sampling distribution of X¯ if n=4 .

Answer 8

b.

To determine

Describe the shape of the sampling distribution of X¯ if n=100 .

Answer 9

b.

To determine

Describe the shape of the sampling distribution of X¯ if n=100 .

Answer 10

c.

To determine

Determine the probability that the sample mean will be less than $315,000 .

Answer 11

c.

To determine

Determine the probability that the sample mean will be less than $315,000 .

Answer 12

d.

To determine

Determine the probability that the sample mean will lie between $295,000 and $310,000 .

Answer 13

d.

To determine

Determine the probability that the sample mean will lie between $295,000 and $310,000 .

Answer 14

Expert Solution & Answer

Answer 15

Expert Solution & Answer

Answer 16

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Answer 17

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Describe the shape of the sampling distribution of X ¯ if n = 4 .

Solution Summary: The author explains the shape of the sampling distribution of stackrel X, which is positively skewed.

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Describe the shape of the sampling distribution of X¯ if n=4 .

Describe the shape of the sampling distribution of X¯ if n=100 .

Determine the probability that the sample mean will be less than $315,000 .

Determine the probability that the sample mean will lie between $295,000 and $310,000 .

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Chapter 7 Solutions