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 7450 hours. The population standard deviation is 700 hours. A random sample of 49 light bulbs indicates a sample mean life of 7,230 hours. a. At the 0.05 level of significance, is there evidence that the mean life is different from 7450 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? e. Compare the results of parts (a) through (d) to those when the standard deviation is 875 hours. a. Let μ be the population mean. Determine the null hypothesis, H0, and the alternative hypothesis, H1. H0: μ ▼ equals= less than or equals≤ greater than or equals≥ not equals≠ enter your response here H1: μ ▼ not equals≠ equals= greater than> less than< 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. Fail to reject H0. There is not sufficient evidence to indicate that the mean life is different from 7450 hours. B. Fail to reject H0. There is sufficient evidence to indicate that the mean life is different from 7450 hours. C. Reject H0. There is not sufficient evidence to indicate that the mean life is different from 7450 hours. D. Reject H0. There is sufficient evidence to indicate that the mean life is different from 7450 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. The p-value is the probability of obtaining a ▼ sample population with a mean ▼ equal to at least as extreme as less extreme than enter your response here hours, given that the ▼ alternative null hypothesis is true. Part 7 c. Construct a 95% confidence interval estimate of the population mean life of the light bulbs. enter your response here≤μ≤enter your response here (Round to the nearest whole number 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 the same. There is sufficient evidence to indicate that the mean life is different from 7450 hours. B. The results of (a) and (c) are not the same. There is not sufficient evidence to indicate that the mean life is different from 7450 hours. C. The results of (a) and (c) are not the same. There is sufficient evidence to indicate that the mean life is different from 7450 hours. D. The results of (a) and (c) are the same. There is not sufficient evidence to indicate that the mean life is different from 7450 hours. Part 9 e. Compare the results of parts (a) through (d) to those when the standard deviation is 875. When the standard deviation is 875, ZSTAT=−1.76, the p-value is 0.078, and the 95% confidence interval is 6,985≤μ≤7,475. State the conclusion for the new standard deviation using the critical value approach. Compare the results to part (a). Using the critical value approach, ▼ reject do not reject H0. This result is ▼ the same as different from the result found in part (a) because ZSTAT has ▼ increased not changed decreased in absolute value. Part 10 State the conclusion for the new standard deviation using the p-value approach. Compare the results to part (b). Using the p-value approach, ▼ do not reject reject H0. This result is ▼ different from the same as the result found in part (b) because the p-value has ▼ not changed. increased. decreased. Part 11 State the conclusion for the new standard deviation using the confidence interval approach. Compare the results to part (c). Using the confidence interval approach, ▼ reject do not reject H0. This result is ▼ different from the same as the result found in part (c), because the confidence interval has ▼ not changed. become narrower. become wider.
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 7450 hours. The population standard deviation is 700 hours. A random sample of 49 light bulbs indicates a sample mean life of 7,230 hours. a. At the 0.05 level of significance, is there evidence that the mean life is different from 7450 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? e. Compare the results of parts (a) through (d) to those when the standard deviation is 875 hours. a. Let μ be the population mean. Determine the null hypothesis, H0, and the alternative hypothesis, H1. H0: μ ▼ equals= less than or equals≤ greater than or equals≥ not equals≠ enter your response here H1: μ ▼ not equals≠ equals= greater than> less than< 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. Fail to reject H0. There is not sufficient evidence to indicate that the mean life is different from 7450 hours. B. Fail to reject H0. There is sufficient evidence to indicate that the mean life is different from 7450 hours. C. Reject H0. There is not sufficient evidence to indicate that the mean life is different from 7450 hours. D. Reject H0. There is sufficient evidence to indicate that the mean life is different from 7450 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. The p-value is the probability of obtaining a ▼ sample population with a mean ▼ equal to at least as extreme as less extreme than enter your response here hours, given that the ▼ alternative null hypothesis is true. Part 7 c. Construct a 95% confidence interval estimate of the population mean life of the light bulbs. enter your response here≤μ≤enter your response here (Round to the nearest whole number 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 the same. There is sufficient evidence to indicate that the mean life is different from 7450 hours. B. The results of (a) and (c) are not the same. There is not sufficient evidence to indicate that the mean life is different from 7450 hours. C. The results of (a) and (c) are not the same. There is sufficient evidence to indicate that the mean life is different from 7450 hours. D. The results of (a) and (c) are the same. There is not sufficient evidence to indicate that the mean life is different from 7450 hours. Part 9 e. Compare the results of parts (a) through (d) to those when the standard deviation is 875. When the standard deviation is 875, ZSTAT=−1.76, the p-value is 0.078, and the 95% confidence interval is 6,985≤μ≤7,475. State the conclusion for the new standard deviation using the critical value approach. Compare the results to part (a). Using the critical value approach, ▼ reject do not reject H0. This result is ▼ the same as different from the result found in part (a) because ZSTAT has ▼ increased not changed decreased in absolute value. Part 10 State the conclusion for the new standard deviation using the p-value approach. Compare the results to part (b). Using the p-value approach, ▼ do not reject reject H0. This result is ▼ different from the same as the result found in part (b) because the p-value has ▼ not changed. increased. decreased. Part 11 State the conclusion for the new standard deviation using the confidence interval approach. Compare the results to part (c). Using the confidence interval approach, ▼ reject do not reject H0. This result is ▼ different from the same as the result found in part (c), because the confidence interval has ▼ not changed. become narrower. become wider.
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 4CYU
Related questions
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
7450
hours. The population standard deviation is
700 hours.
A random sample of
49
light bulbs indicates a sample mean life of
7,230
hours.a. At the
0.05
level of significance, is there evidence that the mean life is different from 7450 hours?b. Compute the p-value and interpret its meaning.
c. Construct a
interval estimate of the population mean life of the light bulbs.
95%
confidence d. Compare the results of (a) and (c). What conclusions do you reach?
e. Compare the results of parts (a) through (d) to those when the standard deviation is
875
hours.a. Let
μ
be the population mean. Determine the null hypothesis,
H0,
and the alternative hypothesis,
H1.
H0:
μ
enter your response here
▼
equals=
less than or equals≤
greater than or equals≥
not equals≠
H1:
μ
enter your response here
▼
not equals≠
equals=
greater than>
less than<
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?
Fail to reject
H0.
There
is not
sufficient evidence to indicate that the mean life is different from
7450
hours.Fail to reject
H0.
There
is
sufficient evidence to indicate that the mean life is different from
7450
hours.Reject
H0.
There
is not
sufficient evidence to indicate that the mean life is different from
7450
hours.Reject
H0.
There
is
sufficient evidence to indicate that the mean life is different from
7450
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.
The p-value is the probability of obtaining a
with a mean
hypothesis is true.
▼
sample
population
▼
equal to
at least as extreme as
less extreme than
enter your response here
hours, given that the
▼
alternative
null
Part 7
c. Construct a 95% confidence interval estimate of the population mean life of the light bulbs.
enter your response here≤μ≤enter your response here
(Round to the nearest whole number as needed.)Part 8
d. Compare the results of (a) and (c). What conclusions do you reach?
The results of (a) and (c) are the same. There
is
sufficient evidence to indicate that the mean life is different from
7450
hours.The results of (a) and (c) are not the same. There
is not
sufficient evidence to indicate that the mean life is different from
7450
hours.The results of (a) and (c) are not the same. There
is
sufficient evidence to indicate that the mean life is different from
7450
hours.The results of (a) and (c) are the same. There
is not
sufficient evidence to indicate that the mean life is different from
7450
hours.Part 9
e. Compare the results of parts (a) through (d) to those when the standard deviation is
875.
When the standard deviation is
875,
ZSTAT=−1.76,
the p-value is
0.078,
and the 95% confidence interval is
6,985≤μ≤7,475.
State the conclusion for the new standard deviation using the critical value approach. Compare the results to part (a).Using the critical value approach,
the result found in part (a) because
in absolute value.
▼
reject
do not reject
H0.
This result is
▼
the same as
different from
ZSTAT
has
▼
increased
not changed
decreased
Part 10
State the conclusion for the new standard deviation using the p-value approach. Compare the results to part (b).
Using the p-value approach,
the result found in part (b) because the p-value has
▼
do not reject
reject
H0.
This result is
▼
different from
the same as
▼
not changed.
increased.
decreased.
Part 11
State the conclusion for the new standard deviation using the confidence interval approach. Compare the results to part (c).
Using the confidence interval approach,
the result found in part (c), because the confidence interval has
▼
reject
do not reject
H0.
This result is
▼
different from
the same as
▼
not changed.
become narrower.
become wider.
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