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

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