A bottled water distributor wants to determine whether the mean amount of water contained in 1-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 per 1-gallon bottle is

0.995

gallon. Complete parts (a) through (d) below.

a. Is there evidence that the mean amount is different from

1.0

gallon? (Use

=0.05.)

Let

be the population mean. Determine the null hypothesis,

H0,

and the alternative hypothesis,

H1.

H0:

equals=

1

H1:

not equals

1

Part 2What is the test statistic?

ZSTAT=negative 1.761.76

(Round to two decimal places as needed.)Part 3What is/are the critical value(s)? (Use

=0.05.)

1.671.67

(Round to two decimal places as needed. Use a comma to separate answers as needed.)Part 4What is the final conclusion?

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

isnot

sufficient evidence that the mean amount is different from

1.0

gallon.

C.

Failtoreject

H0.

There

is

sufficient evidence to warrant rejection of the claim 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.

Part 5b. Compute the p-value and interpret its meaning.What is the p-value?

0.070.07

(Round to three decimal places as needed.)Part 6Interpret the meaning of the p-value. Choose the correct answer below.

A.

Reject

H0.

There

is

sufficient evidence to warrant rejection of the claim that the mean amount is equal to

1

gallon.

B.

Failtoreject

H0.

There

isnot

sufficient evidence to warrant rejection of the claim that the mean amount is equal to

1

gallon.

C.

Reject

H0.

There

isnot

sufficient evidence to warrant rejection of the claim that the mean amount is equal to

1

gallon.

D.

Failtoreject

H0.

There

is

sufficient evidence to warrant rejection of the claim that the mean amount is equal to

1

gallon.

Part 7c. Construct a

95%

confidence interval estimate of the population mean amount of water per 1-gallon bottle.

enter your response hereenter your response here

(Round to four decimal places as needed.)Part 8d. Compare the results of (a) and (c). What conclusions do you reach?

A.

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

B.

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

C.

No meaningful conclusions can be reached.