Question

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

.03 gallon. You select a random sample of 50 ​bottles, and the mean amount of water per​ 1-gallon bottle is 0.993 gallon. Complete parts​ (a) through​ (d) below.

a. Is there evidence that the mean amount is different from 1 ​gallon? (Use alphaαequals=0.01)

Let muμ be the population mean. Determine the null​ hypothesis,

What is the test​ statistic? Upper Z Subscript STATequals negative 0.94 ​(Round to two decimal places as​ needed.)

What​ is/are the critical​ value(s)? (Use alphaequals0.05​.) ​(Round to two decimal places as needed. Use a comma to separate answers as​ needed.)

What is the final​ conclusion? A. Fail to reject Upper H 0. There is not sufficient evidence that the mean amount is different from 1.0 gallon.B. Reject Upper H 0. There is not sufficient evidence to warrant rejection of the claim that the mean amount is different from 1.0 gallon. C. Reject Upper H 0. There is sufficient evidence to warrant rejection of the claim that the mean amount is different from 1.0 gallon. D. Fail to reject Upper H 0. There is sufficient evidence to warrant rejection of the claim that the mean amount is different from 1.0 gallon.

b. Compute the​ p-value and interpret its meaning. What is the​ p-value? ​(Round to three decimal places as​ needed.)

Interpret the meaning of the​ p-value. Choose the correct answer below. A. Reject Upper H 0. There is not sufficient evidence to warrant rejection of the claim that the mean amount is equal to 1 gallon. Your answer is not correct.B. Fail to reject Upper H 0. There is not sufficient evidence to warrant rejection of the claim that the mean amount is equal to 1 gallon. This is the correct answer.C. Reject Upper H 0. There is sufficient evidence to warrant rejection of the claim that the mean amount is equal to 1 gallon. D. Fail to reject Upper H 0. There is sufficient evidence to warrant rejection of the claim that the mean amount is equal to 1 gallon. c. Construct a 95​% confidence interval estimate of the population mean amount of water per​ 1-gallon bottle. 0.9877less than or equalsmuless than or equals 1.0043 ​(Round to four decimal places as​ needed.) d. Compare the results of​ (a) and​ (c). What conclusions do you​ reach? A. The results of​ (a) and​ (c) are the same. This is the correct answer.B. The results of​ (a) and​ (c) are not the same. C. No meaningful conclusions can be reached.

Answer 1

H0 : mu = 1
HA: mu not equasl to 1

test statistics:

z = ( x - mean)/(s/sqrt(n))
= ( 0.993 - 1)/(0.03/sqrt(50))
= -1.65

critical value = +/- 2.58

Reejct H0 if z < -2.58 or z > 2.58

A. Fail to reject Upper H 0. There is not sufficient evidence that the mean amount is different from 1.0 gallon

b)

p value = .0989

B. Fail to reject Upper H 0. There is not sufficient evidence to warrant rejection of the claim that the mean amount is equal to 1 gallon.

c)

z value at 95% = 1.96

CI = mean +/- z *(s/sqrt(n))
= 0.993 +/- 1.96 *(0.03/sqrt(50))
= (0.9847,1.0013)

d)

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

because confidence interval contain hypothesised value 1