The quality-control manager at a compact fluorescent light bulb (CFL) factory needs to determine whether the mean life of a large shipment of CFLs is equal to 7,538 hours. The population standard deviation is 92 hours. A random sample of 64 light bulbs indicates a sample mean life of 7515 hours. a. At the 0.05 level of significance, is there evidence that the mean life is different from 7,538 hours. b. Compute the p-value and interpret its meaning. c. Construct a 95% confidence interval estimate of the population mean life of the light bulbs. d. Compare the results of (a) and (c). What conclusions do you reach?

a. Let be the population mean. Determine the null hypothesis, H_0, and the alternative hypothesis, H_1. H_0: = blank H_1: blank

What is the test statistic?

Z_STAT = blank (Round to two decimal places as needed

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

What is the final conclusion?

A. Reject H_0 There is not sufficient evidence to prove that the mean life is different from 7,538 hours.

B. Fail to reject H_0. There is sufficient evidence to prove that the mean life is different from 7,538 hours

C. Reject H_0. There is sufficient evidence to prove that the mean life is different from 7,538 hours.

D. Fail to reject H_0. There is not sufficient evidence to prove that the mean life is different from 7,538 hours.

b. 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. Fail to reject H_0. There is not sufficient evidence to prove that the mean life is different from 7,538 hours

B. Reject H_0. There is not sufficient evidence to prove that the mean life is different from 7,538 hours.

C. Reject H_0 There is sufficient evidence to prove that the mean life is different from 7,538 hours

D. Fail to reject Ho There is sufficient evidence to prove that the mean life is different from 7,538 hours.

c. Construct a 95% confidence interval estimate of the population mean life of the light bulbs. (Round to one decimal place as needed.)

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

A. The results of (a) and (c) are not the same: there is sufficient evidence to prove that the mean life is different from 7,538 hours.

B. The results of (a) and (c) are the same: there is sufficient evidence to prove that the mean life is different from 7,538 hours.

C. The results of (a) and (c) are not the same: there is not sufficient evidence to prove that the mean life is different from 7,538 hours.

D. The results of (a) and (c) are the same: there is not sufficient evidence to prove that the mean life is different from 7,538 hours.