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 7463 hours. The population standard deviation is 1080 hours. A random sample of 81 light bulbs indicates a sample mean life of 7163 hours.a. At the 0.05 level of significance, is there evidence that the mean life is different from 7 comma 463 hours question markb. 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 mu be the population mean. Determine the nullhypothesis, Upper H 0, and the alternative hypothesis, Upper H 1.Upper H 0: Upper H 1:What is the test statistic?Upper Z STAT (Round to two decimal places as needed.)What is/are the critical value(s)? (Round to two decimal places as needed. Use a comma to separate answers as needed.)What is the final conclusion?A. Reject Upper H 0. There is sufficient evidence to prove that the mean life is different from 7463 hours.B. Fail to reject Upper H 0. There is sufficient evidence to prove that the mean life is different from 7463 hours.C. Fail to reject Upper H 0. There is not sufficient evidence to prove that the mean life is different from 7463 hours.D. Reject Upper H 0. There is not sufficient evidence to prove that the mean life is different from 7463 hours.b. What is the p-value? (Round to three decimal places asneeded.)Interpret the meaning of the p-value. Choose the correct answer below.A. Fail to reject Upper H 0. There is not sufficient evidence to prove that the mean life is different from 7463 hours.B. Reject Upper H 0. There is sufficient evidence to prove that the mean life is different from 7463 hours.C. Reject Upper H 0. There is not sufficient evidence to prove that the mean life is different from 7463 hours.D. Fail to reject Upper H 0. There is sufficient evidence to prove that the mean life is different from 7463 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 the same: there is not sufficient evidence to prove that the mean life is different from 7463 hours.B. The results of (a) and (c) are the same: there is sufficient evidence to prove that the mean life is different from 7463 hours.C. The results of (a) and (c) are not the same: there is sufficient evidence to prove that the mean life is different from 7463 hours.D. The results of (a) and (c) are not the same: there is not sufficient evidence to prove that the mean life is different from 7463 hours.

At the 0.05 level of significance, the the result is significant because 0.0124<0.05. There is significant evidence that mean life of light bulbs is different than 7463 hours.

95% Confidence Interval can be calculated using M±ME where

M is the sample mean life of a large shipment of CFLs (7163 hours)

ME is the margin of error from the mean

margin of error (ME) from the mean can be calculated using the formula

ME=[tex]\frac{z*s}{\sqrt{N} }[/tex] where

z is the corresponding statistic in the 95% confidence level (1.96)

s is the standard deviation of the sample (1080 hours)

N is the sample size (81)

Then ME=[tex]\frac{1.96*1080}{\sqrt{81} }[/tex] =235.2

Thus 95% confidence interval estimate of the population mean life of the light bulbs is 7163±235.2 hours. That is between 6927.8 and 7398.2 hours.