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d. Construct a 95% confidence interval estimate. How does this change your answer to part (b)?

d. Construct a 95% confidence interval estimate. How does this change your answer to part (b)?

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section: Chapter Questions
Problem 8SGR
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Please answer for the boxes in part D. I've had to repost this question 3 times.
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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