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The manager of a paint supply store wants to estimate the actual amount of paint contained in 1-gallon cans purchased from a nationally known manufacturer. The manufacturer's specifications state that the standard deviation of the amount of paint is equal to 0.02 gallon. A random sample of 50 cans is selected, and he sample mean amount of paint per 1-gallon can is 0.987 gallon. Complete parts (a) through (d). a. Construct a 99% confidence interval estimate for the population mean amount of paint included in a 1-gallon can. 0.97971 sus 0.99429 Round to five decimal places as needed.) p. On the basis of these results, do you think the manager has a right to complain to the manufacturer? Why? Yes, because a 1-gallon paint can containing exactly 1-gallon of paint lies outside the 99% confidence interval. C. Must you assume that the population amount of paint per can is normally distributed here? Explain. OA. Yes, because the Central Limit Theorem almost always ensures that X is normally distributed when n is large. In this case, the value of n is small. B. No, because the Central Limit Theorem almost always ensures that X is normally distributed when n is large. In this case, the value of n is large. OC. No, because the Central Limit Theorem almost always ensures that X is normally distributed when n is small. In this case, the value of n is small. O D. Yes, since nothing is known about the distribution of the population, it must be assumed that the population is normally distributed. d. Construct a 95% confidence interval estimate. How does this change your answer to part (b)? (Round to five decimal places as needed.)

The manager of a paint supply store wants to estimate the actual amount of paint contained in 1-gallon cans purchased from a nationally known manufacturer. The manufacturer's specifications state that the standard deviation of the amount of paint is equal to 0.02 gallon. A random sample of 50 cans is selected, and he sample mean amount of paint per 1-gallon can is 0.987 gallon. Complete parts (a) through (d). a. Construct a 99% confidence interval estimate for the population mean amount of paint included in a 1-gallon can. 0.97971 sus 0.99429 Round to five decimal places as needed.) p. On the basis of these results, do you think the manager has a right to complain to the manufacturer? Why? Yes, because a 1-gallon paint can containing exactly 1-gallon of paint lies outside the 99% confidence interval. C. Must you assume that the population amount of paint per can is normally distributed here? Explain. OA. Yes, because the Central Limit Theorem almost always ensures that X is normally distributed when n is large. In this case, the value of n is small. B. No, because the Central Limit Theorem almost always ensures that X is normally distributed when n is large. In this case, the value of n is large. OC. No, because the Central Limit Theorem almost always ensures that X is normally distributed when n is small. In this case, the value of n is small. O D. Yes, since nothing is known about the distribution of the population, it must be assumed that the population is normally distributed. d. Construct a 95% confidence interval estimate. How does this change your answer to part (b)? (Round to five decimal places as needed.)

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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The manager of a paint supply store wants to estimate the actual amount of paint contained in 1-gallon cans purchased from a nationally known manufacturer. The manufacturer's specifications state that the standard deviation of the amount of paint is equal to 0.02 gallon. A random sample of 50 cans is selected, and the sample mean amount of paint per 1-gallon can is 0.987 gallon. Complete parts (a) through (d). a. Construct a 99% confidence interval estimate for the population mean amount of paint included in a 1-gallon can. 0.97971 sus 0.99429 (Round to five decimal places as needed.) b. On the basis of these results, do you think the manager has a right to complain to the manufacturer? Why? Yes, because a 1-gallon paint can containing exactly 1-gallon of paint lies outside the 99% confidence interval. c. Must you assume that the population amount of paint per can is normally distributed here? Explain. O A. Yes, because the Central Limit Theorem almost always ensures that X is normally distributed when n is large. In this case, the value of n is small. B. No, because the Central Limit Theorem almost always ensures that X is normally distributed when n is large. In this case, the value of n is large. O C. No, because the Central Limit Theorem almost always ensures that X is normally distributed when n is small. In this case, the value of n is small. O D. Yes, since nothing is known about the distribution of the population, it must be assumed that the population is normally distributed. d. Construct a 95% confidence interval estimate. How does this change your answer to part (b)? (Round to five decimal places as needed.)
Transcribed Image Text:The manager of a paint supply store wants to estimate the actual amount of paint contained in 1-gallon cans purchased from a nationally known manufacturer. The manufacturer's specifications state that the standard deviation of the amount of paint is equal to 0.02 gallon. A random sample of 50 cans is selected, and the sample mean amount of paint per 1-gallon can is 0.987 gallon. Complete parts (a) through (d). a. Construct a 99% confidence interval estimate for the population mean amount of paint included in a 1-gallon can. 0.97971 sus 0.99429 (Round to five decimal places as needed.) b. On the basis of these results, do you think the manager has a right to complain to the manufacturer? Why? Yes, because a 1-gallon paint can containing exactly 1-gallon of paint lies outside the 99% confidence interval. c. Must you assume that the population amount of paint per can is normally distributed here? Explain. O A. Yes, because the Central Limit Theorem almost always ensures that X is normally distributed when n is large. In this case, the value of n is small. B. No, because the Central Limit Theorem almost always ensures that X is normally distributed when n is large. In this case, the value of n is large. O C. No, because the Central Limit Theorem almost always ensures that X is normally distributed when n is small. In this case, the value of n is small. O D. Yes, since nothing is known about the distribution of the population, it must be assumed that the population is normally distributed. d. Construct a 95% confidence interval estimate. How does this change your answer to part (b)? (Round to five decimal places as needed.)
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