Question

3. 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 7,545 hours. The population standard deviation is 900 hours. A random sample of 81 light bulbs indicates a sample mean life of 7,295 hours. a. At the 0.05 level of significance, is there evidence that the mean life is different 7,545 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, H0, and the alternative hypothesis, H1. H0: ?=____ H1: ?? What is the test statistic? ZSTAT=_ (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?____ Fail to reject H0. There is sufficient evidence to prove that the mean life is different from 7,545 hours. Reject H0. There is not sufficient evidence to prove that the mean life is different from 7,545 hours. Reject H0. There is sufficient evidence to prove that the mean life is different from 7,545 hours. Fail to reject H0. There is not sufficient evidence to prove that the mean life is different from 7,545 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 H0. There is not sufficient evidence to prove that the mean life is different from 7,545 hours. b. Fail to reject H0. There is sufficient evidence to prove that the mean life is different from 7,545 hours. c. Reject H0. There is sufficient evidence to prove that the mean life is different from 7,545 hours. d. Reject H0. There is not sufficient evidence to prove that the mean life is different from 7,545 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 7,545 hours. b. The results of (a) and (c) are not the same: there Is sufficient evidence to prove that the mean life is different from 7,545 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 7,545 hours. d. The results of (a) and (c) are the same: there Is sufficient evidence to prove that the mean life is different from 7,545 hours.

          3. 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 7,545 hours. The population
standard deviation is 900 hours. A random sample of 81 light
bulbs indicates a sample mean life of 7,295 hours.
a. At the 0.05 level of significance, is there
evidence that the mean life is different 7,545 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, H0, and the alternative hypothesis, H1.
H0: ?=________
H1: ??________
What is the test statistic?
ZSTAT=_________ (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?__________________
Fail to reject H0. There is sufficient evidence to
prove that the mean life is different from 7,545 hours.
Reject H0. There is not sufficient evidence to prove that
the mean life is different from 7,545 hours.
Reject H0. There is sufficient evidence to prove that the mean
life is different from 7,545 hours.
Fail to reject H0. There is not sufficient
evidence to prove that the mean life is different from 7,545
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 H0. There is not sufficient
evidence to prove that the mean life is different from 7,545
hours.
b. Fail to reject H0. There is sufficient evidence to prove that
the mean life is different from 7,545 hours.
c. Reject H0. There is sufficient evidence to prove that the
mean life is different from 7,545 hours.
d. Reject H0. There is not sufficient evidence to prove
that the mean life is different from 7,545 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 7,545 hours.
b. The results of  (a) and  (c) are not the same:
there Is sufficient evidence to prove that the mean life is
different from 7,545 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 7,545 hours.
d. The results of  (a) and  (c) are the same: there Is
sufficient evidence to prove that the mean life is different from
7,545 hours.

Added by Jonathan C.

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