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 0.02 gallon. You select a random sample of 45 bottles, and the mean amount of water per 1-gallon bottle is 0.994 gallon. Complete parts (a) through (d) below. a. Is there evidence that the mean amount is different from 1.0 gallon? (Use α-0.05) Let u be the population mean. Determine the null hypothesis, Ho, and the alternative hypothesis, H What is the test statistic? STAT-J (Round to two decimal places as needed ) What is/are the critical value(s)? (Use α = 0.05.) Round to two decimal places as needed. Use a comma to separate answers as needed.) What is the final conclusion? O A. Reject Ho. There is sufficient evidence that the mean amount is different from 1.0 gallon OB. Fail to reject Ho. There is sufficient evidence to warrant rejection of the claim that the mean amount is different from 1.0 galon Reject Ho There is not sufficient evidence to warrant rejection of the claim that the mean amount is different from 1.0 gallon. Fail to reject Ho There is not sufficient evidence to warrant re ection of the claim that the mean amount is different from 10 gallon C. O D. 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. O A. Fail to reject Ho. There is sufficient evidence to warrant rejection of the claim that the mean amount is equal to 1 gallon ( B. Reject Ho . There is sufficient evidence to warrant rejection of the claim that the mean amount is equal to 1 gallon. OC. Reject Ho. There is not sufficient evidence to warrant rejection of the claim that the mean amount is equal to 1 gallon 0 D. Fail to reject Ho. There is not 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 ] $15 [ ] (Round to four decimal places as needed.) d. Compare the results of (a) and (c). What conclusions do you reach? OA. O B. ° C. The results of (a) and (c) are the same. The results of (a) and (c) are not the same. No meaningful conclusions can be reached.

Answer 1

a)

Ho : mu = 1
Ha: mu not =1

Zstat = (xbar -mu)/(sigma/sqrt(n)
= ( 0.994 -1)/(0.02/sqrt(45))
= -2.01

Critical values are (-1.96 , 1.96)

Decision:
Reject H0 if z < -1.96 or z > 1.96

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

b)

p value = 0.044
Reject H0. There is sufficient evidence to warrant rejection of the claim that the mean amount is different from 1 gallon

c)

The z value at 95% confidence interval is,

alpha = 1 - 0.95 = 0.05
alpha/2 = 0.05/2 = 0.025
Zalpha/2 = Z0.025 = 1.96

Margin of error = E =z *(s/sqrt(n))
= 1.96 *(0.02/sqrt(45))
= 0.0058

CI = mean +/- E
= 0.994 +/- 0.0058

= (0.9882 , 0.9998)

0.9882 <= mu < = 0.9998

d)

The results of a) and C) are same