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

7,457

hours. The population standard deviation is

900hours.

A random sample of

81

light bulbs indicates a sample mean life of

7,207

hours.

a. At the

0.05

level of significance, is there evidence that the mean life is different from 7,457hours?

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?

Question content area bottom

Part 1

a. Let

be the population mean. Determine the null hypothesis,

H0,

and the alternative hypothesis,

H1.

H0:

=enter your response here

H1:

enter your response here

Part 2

What is the test statistic?

ZSTAT=enter your response here

(Round to two decimal places as needed.)

Part 3

What is/are the critical value(s)?

enter your response here

(Round to two decimal places as needed. Use a comma to separate answers as needed.)

Part 4

What is the final conclusion?

A.

Reject

H0.

There

is

sufficient evidence to prove that the mean life is different from

7,457

hours.

B.

Failtoreject

H0.

There

is

sufficient evidence to prove that the mean life is different from

7,457

hours.

C.

Failtoreject

H0.

There

isnot

sufficient evidence to prove that the mean life is different from

7,457

hours.

D.

Reject

H0.

There

isnot

sufficient evidence to prove that the mean life is different from

7,457

hours.

Part 5

b. What is the p-value?

enter your response here

(Round to three decimal places as needed.)

Part 6

Interpret the meaning of the p-value. Choose the correct answer below.

A.

Failtoreject

H0.

There

isnot

sufficient evidence to prove that the mean life is different from

7,457

hours.

B.

Reject

H0.

There

is

sufficient evidence to prove that the mean life is different from

7,457

hours.

C.

Failtoreject

H0.

There

is

sufficient evidence to prove that the mean life is different from

7,457

hours.

D.

Reject

H0.

There

isnot

sufficient evidence to prove that the mean life is different from

7,457

hours.

Part 7

c. Construct a 95% confidence interval estimate of the population mean life of the light bulbs.

enter your response hereenter your response here

(Round to one decimal place as needed.)

Part 8

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

7,457

hours.

B.

The results of (a) and (c) are the same: there

isnot

sufficient evidence to prove that the mean life is different from

7,457

hours.

C.

The results of (a) and (c) are not the same: there

isnot

sufficient evidence to prove that the mean life is different from

7,457

hours.

D.

The results of (a) and (c) are the same: there

is

sufficient evidence to prove that the mean life is different from

7,457

hours.