Question

A bottled water distributor wants to estimate the amount of water contained in 1​-gallon bottles purchased from a nationally known water bottling company. The water bottling​ company's specifications state that the standard deviation of the amount of water is equal to 0.02 gallon. A random sample of 50 bottles is​ selected, and the sample mean amount of water per 1​-gallon bottle is 0.979 gallon.

a. Construct a 95​% confidence interval estimate for the population mean amount of water included in a​ 1-gallon bottle

? ≤ μ ≤ ?

​(Round to five decimal places as​ needed.)

b. On the basis of these​ results, do you think that the distributor has a right to complain to the water bottling​ company? Why?

(Yes or No), because a​ 1-gallon bottle containing exactly​ 1-gallon of water lies (outside or within) the 95% confidence interval.

c.  Must you assume that the population amount of water per bottle is normally distributed​ here? Explain. (Choose the answer below)

A. ​Yes, because the Central Limit Theorem almost always ensures that overbarX 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 overbarX is normally distributed when n is large. In this​case, the value of n is large

C. ​No, because the Central Limit Theorem almost always ensures that overbarX is normally distributed when n is small. In this​case, the value of n is small.

D. ​Yes, since nothing is known about the distribution of the​population, it must be assumed that the population is normally distributed.

part d. Construct a 90​% confidence interval estimate. How does this change your answer to part​ (b)?

? ≤ μ ≤ ?

​(Round to five decimal places as​ needed.)

How does this change your answer to part​ (b)?

A​ 1-gallon bottle containing exactly​ 1-gallon of water lies (outside or within) the 90​% confidence interval. The distributor (still has or now has or now does not have or still does not have) a right to complain to the bottling company.

Answer 1

b. No, because a​ 1-gallon bottle containing exactly​ 1-gallon of water lies outside the 95% confidence interval.

c. Option: B. ​No, because the Central Limit Theorem almost always ensures that overbarX is normally distributed when n is large. In this​case, the value of n is large.

1-gallon bottle containing exactly​ 1-gallon of water lies outside the 90​% confidence interval. The distributor still does not have a right to complain to the bottling company.