A bottled water distributor wants to determine whether the mean amount of water contained in1-gallon bottles purchased from a nationally known water bottling company is actually 1 gallon. You know from the water bottling company specifications that the standard deviation of the amount of water is 0.02 gallon. You select a random sample of 50 bottles, and the mean amount of water per1-gallon bottle is 0.993 gallon. Complete parts(a) through(d) below.

a. Is there evidence that the mean amount is different from 1.0 gallon? (Use =0.01.)

Let be the population mean. Determine the nullhypothesis, H0, and the alternativehypothesis, H1.

What is the teststatistic? (Round to two decimal places asneeded.)

Whatis/are the criticalvalue(s)? (Use =0.01.) (Round to two decimal places as needed. Use a comma to separate answers asneeded.)

What is the finalconclusion?

A. Reject H0. There is sufficient evidence to warrant rejection of the claim that the mean amount is different from 1.0 gallon.

B. Failtoreject H0. There is sufficient evidence to warrant rejection of the claim that the mean amount is different from 1.0 gallon.

C. Failtoreject H0. There isnot sufficient evidence that the mean amount is different from 1.0 gallon.

D .Reject H0. There isnot sufficient evidence to warrant rejection of the claim that the mean amount is different from 1.0 gallon

b. Compute thep-value and interpret its meaning.

What is thep-value? (Round to three decimal places asneeded.)

Interpret the meaning of thep-value. Choose the correct answer below.

1. Reject H0. There is sufficient evidence to warrant rejection of the claim that the mean amount is equal to 1 gallon.

2. Failtoreject H0. There isnot sufficient evidence to warrant rejection of the claim that the mean amount is equal to 1 gallon.

3. Failtoreject H0. There is sufficient evidence to warrant rejection of the claim that the mean amount is equal to 1 gallon.

4. Reject H0. There isnot sufficient evidence to warrant rejection of the claim that the mean amount is equal to 1 gallon.

c. Construct a 99% confidence interval estimate of the population mean amount of water per1-gallon bottle.

d. Compare the results of(a) and(c). What conclusions do youreach?

1. The results of(a) and(c) are the same.

2. The results of(a) and(c) are not the same.

3. No meaningful conclusions can be reached.