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 0.03 gallon. A random sample of 50 bottles is​ selected, and the sample mean amount of water per 1​-gallon bottle is 0.941 gallon. Complete parts​ (a) through​ (d).

a. Construct a 99​% confidence interval estimate for the population mean amount of water included in a​ 1-gallon bottle. nothingless than or equalsmuless than or equals nothing

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

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

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

Answer 1

a)

b) Since upper bound of the confidence interval< 1, so the average amount of water per bottle is significantly less than 1 gallon, so the distributor has a right to complain to the water bottling​ company.

c) Since sample size is large enough ( > 30),we can approximate the sampling distribution of sample mean by normal distribution, using Central limit theorem. So, assumption is not necessary.

d)

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