Question

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 7529 hours. The population standard deviation is 1000 hours. A random sample of 64 light bulbs indicates a sample mean life of 7504 hours.

1. Let mu be the population mean. Determine the null​hypothesis, Upper H 0​, and the alternative​ hypothesis, Upper H 1.

Upper H 0​:

Upper H 1​:

2. What is the test​ statistic?

3. Upper Z STAT ​(Round to two decimal places as​ needed.)

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

5. What is the final​ conclusion?

A. Reject Upper H 0. There is sufficient evidence to prove that the mean life is different from 7529 hours.

B. Fail to reject Upper H 0. There is sufficient evidence to prove that the mean life is different from 7529 hours.

C. Fail to reject Upper H 0. There is not sufficient evidence to prove that the mean life is different from 7529 hours.

D. Reject Upper H 0. There is not sufficient evidence to prove that the mean life is different from 7529 hours.

6. What is the​ p-value? ​(Round to three decimal places as​needed.)

7. 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 7529 hours.

B. Reject Upper H 0. There is sufficient evidence to prove that the mean life is different from 7529 hours.

C. Reject Upper H 0. There is not sufficient evidence to prove that the mean life is different from 7529 hours.

D. Fail to reject Upper H 0. There is sufficient evidence to prove that the mean life is different from 7529 hours.

8 . 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 7529 hours.

B. The results of​ (a) and​ (c) are the​ same: there is sufficient evidence to prove that the mean life is different from 7529 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 7529 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 7529 hours.

Answer 1

4.)

Significance() is not given, so taking default value 0.05\\\\

hence

Confidence =1-0.05=0.95=95%

at 95% confidence critical values=(-1.96, 1.96)

5.)

C. Fail to reject Upper H 0. There is not sufficient evidence to prove that the mean life is different from 7529 hours.

6.)

p-value=P(|Z|<-0.20)=2*P(Z<-0.20)=0.841

7.)

A. Fail to reject Upper H 0. There is not sufficient evidence to prove that the mean life is different from 7529 hours.