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 7,472 hours. The population standard deviation is 1,080 hours. A random sample of 81 light bulbs indicates a sample mean life of 7,172 hours. a. At the 0.05 level of significance, is there evidence that the mean life is different from 7,472 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 μ be the population mean. Determine the null hypothesis, H0, and the alternative hypothesis, H1. H0: μ= H1: μ≠ 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? A. Fail to reject H0. There is sufficient evidence to prove that the mean life is different from 7,472 hours. B. Reject H0. There is sufficient evidence to prove that the mean life is different from 7,472 hours. C. Reject H0. There is not sufficient evidence to prove that the mean life is different from 7,472 hours. D. Fail to reject H0. There is not sufficient evidence to prove that the mean life is different from 7,472 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 7,472 hours. B. Reject H0. There is sufficient evidence to prove that the mean life is different from 7,472 hours. C. Fail to reject H0. There is sufficient evidence to prove that the mean life is different from 7,472 hours. D. Reject H0. There is not sufficient evidence to prove that the mean life is different from 7,472 hours. c. Construct a 95% confidence interval estimate of the population mean life of the light bulbs. ?≤μ≤? (Round to one decimal place as needed.)
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 7,472 hours. The population standard deviation is 1,080 hours. A random sample of 81 light bulbs indicates a sample mean life of 7,172 hours. a. At the 0.05 level of significance, is there evidence that the mean life is different from 7,472 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 μ be the population mean. Determine the null hypothesis, H0, and the alternative hypothesis, H1. H0: μ= H1: μ≠ 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? A. Fail to reject H0. There is sufficient evidence to prove that the mean life is different from 7,472 hours. B. Reject H0. There is sufficient evidence to prove that the mean life is different from 7,472 hours. C. Reject H0. There is not sufficient evidence to prove that the mean life is different from 7,472 hours. D. Fail to reject H0. There is not sufficient evidence to prove that the mean life is different from 7,472 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 7,472 hours. B. Reject H0. There is sufficient evidence to prove that the mean life is different from 7,472 hours. C. Fail to reject H0. There is sufficient evidence to prove that the mean life is different from 7,472 hours. D. Reject H0. There is not sufficient evidence to prove that the mean life is different from 7,472 hours. c. Construct a 95% confidence interval estimate of the population mean life of the light bulbs. ?≤μ≤? (Round to one decimal place as needed.)
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.5: Comparing Sets Of Data
Problem 13PPS
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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
7,472
hours. The population standard deviation is
1,080 hours.
A random sample of
81
light bulbs indicates a sample mean life of
7,172
hours.a. At the
0.05
level of significance, is there evidence that the mean life is different from 7,472 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
μ
be the population mean. Determine the null hypothesis,
H0,
and the alternative hypothesis,
H1.
H0:
μ=
H1:
μ≠
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
7,472
hours.Reject
H0.
There
is
sufficient evidence to prove that the mean life is different from
7,472
hours.Reject
H0.
There
is not
sufficient evidence to prove that the mean life is different from
7,472
hours.Fail to reject
H0.
There
is not
sufficient evidence to prove that the mean life is different from
7,472
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.
Fail to reject
H0.
There
is not
sufficient evidence to prove that the mean life is different from
7,472
hours.Reject
H0.
There
is
sufficient evidence to prove that the mean life is different from
7,472
hours.Fail to reject
H0.
There
is
sufficient evidence to prove that the mean life is different from
7,472
hours.Reject
H0.
There
is not
sufficient evidence to prove that the mean life is different from
7,472
hours.c. Construct a 95% confidence interval estimate of the population mean life of the light bulbs.
?≤μ≤?
(Round to one decimal place as needed.)Expert Solution
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