Download Online 16 - Section 9.3

Online 16 - Section 9.3-Doug Ensley
Student: _____________________
Date: _____________________
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Instructor: Doug Ensley
Course: MAT117 01 Applied Statistics Ensley
Assignment: Online 16 - Section 9.3
Online 16 - Section 9.3-Doug Ensley
1. When 897 male workers were asked how many hours they worked in the previous week, the mean was 45.7 with a
standard deviation of 14.7. Does this suggest that the population mean work week for men exceeds 40 hours? Answer by
completing parts (a) through (d).
a. Identify the relevant variable and parameter. Choose the correct relevant variable below.
A. The relevant variable is the maximum number of hours worked in a week.
B. The relevant variable is the number of hours worked in the previous week by male workers.
C. The relevant variable is the population mean work week (in hours) for men.
Choose the correct parameter below.
A. The parameter of interest is the population mean work week (in hours) for men.
B. The parameter of interest is the maximum number of hours worked in a week.
C. The parameter of interest is the number of hours worked in the previous week by male workers.
b. State the null hypothesis.
A. H 0 : μ ≠ 40
B. H 0 : μ < 40
C. H 0 : μ > 40
D. H 0 : μ = 40
State the alternative hypothesis.
A. H a : μ < 40
B. H a : μ = 40
C. H a : μ ≠ 40
D. H a : μ > 40
c. Report and interpret the P-value for the test statistic value of t = 11.6.
P-value =
(Round to the nearest thousandth as needed.)
Interpret the P-value. Choose the correct interpretation below.
A. The P-value is the probability of obtaining a sample with a mean of 45.7 or more hours assuming
the alternative hypothesis were true.
B. The P-value is the probability of obtaining a sample with a mean of 40 or more hours assuming
the null hypothesis were true.
C. The P-value is the probability of obtaining a sample with a mean of 40 or more hours assuming
the alternative hypothesis were true.
D. The P-value is the probability of obtaining a sample with a mean of 45.7 or more hours assuming
the null hypothesis were true.
d. Explain how to make a decision for the significance level of 0.01.
A. Since the P-value is less than the significance level of 0.01, there is sufficient evidence to reject
the null hypothesis and to conclude that the population mean work week for men exceeds 40
hours.
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B. Since the P-value is less than the significance level of 0.01, there is sufficient evidence to accept
the null hypothesis and to conclude that the population mean work week for men less than 40
Online 16 - Section 9.3-Doug Ensley
hours.
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Online 16 - Section 9.3-Doug Ensley
2. When 186 workers aged 18-25 were asked how many hours they worked in the previous week, the mean was 37.73 with a
standard deviation of 13.51. Does this suggest that the population mean work week for this age group differs from 40
hours? Answer by completing parts a through d.
a. Identify the relevant and parameter variable. Choose the correct relevant variable below.
A. The relevant variable is the population mean work week (in hours) for workers aged 18-25.
B. The relevant variable is the 186 workers.
C. The relevant variable is the maximum number of hours worked in a week.
D. The relevant variable is the number of hours worked in the previous week by workers aged
18-25.
Identify the parameter. Choose the correct parameter below.
A. The parameter of interest is the population mean work week (in hours) for workers aged 18-25.
B. The parameter of interest is the maximum number of hours worked in a week.
C. The parameter of interest is the number of hours worked in the previous week by workers aged
18-25.
D. The parameter of interest is the 186 workers.
b. State the null and alternative hypotheses.
State the null hypothesis. Choose the correct answer below.
A. H 0 : μ = 40
B. H 0 : μ > 40
C. H 0 : μ < 40
D. H 0 : μ ≠ 40
State the alternative hypothesis. Choose the correct answer below.
A. H a : μ ≠ 40
B. H a : μ = 40
C. H a : μ > 40
D. H a : μ < 40
c. Find the test statistic value.
t=
(Round to two decimal places as needed.)
Interpret the test statistic value. Choose the correct answer below.
A. The sample mean is 2.29 standard errors above the mean hypothesized in the null hypothesis.
B. The sample mean is 2.29 standard errors below the mean hypothesized in the alternative
hypothesis.
C. The sample mean is 2.29 standard errors below the mean hypothesized in the null hypothesis.
D. The sample mean is 2.29 standard errors above the mean hypothesized in the alternative
hypothesis.
d. Report the P-value and state the conclusion in context.
4 of 9 Report the P-value.
Online 16 - Section 9.3-Doug Ensley
P-value =
(Round to three decimal places as needed.)
State the conclusion in context. Use a significance level of 0.05. Choose the correct answer below.
A. The P-value is less than the significance level so do not reject the null hypothesis. There is not
significant evidence that the population mean work week differs from 40 hours.
B. The P-value is less than the significance level so reject the null hypothesis. There is significant
evidence that the population mean work week differs from 40 hours.
C. The P-value is greater than the significance level so do not reject the null hypothesis. There is
not significant evidence that the population mean work week differs from 40 hours.
D. The P-value is greater than the significance level so reject the null hypothesis. There is
significant evidence that the population mean work week differs from 40 hours.
3. In an experiment with 10 pairs of stores, the difference in the month's increased sales between the store that used coupons
and the store with the outside poster had a mean of $2798. Use the output shown to test that the population mean
difference is 0, carrying out the five steps of a significance test. Make a decision using a 0.05 significance level.
Test of mu = 0 vs. mu ≠ 0
Variable
N
Mean
StDev SE
Sales
10
2798
3514 1111.22
Variable
95.0% CI
T
P
Sales
(2792.3,2803.7) 2.518 0.03288
State the assumptions for a significance test of a population mean.
A. The variable is quantitative, and the population distribution is approximately normal.
B. The variable is categorical, the data production employs randomization, and the population
distribution is approximately normal.
C. The variable is quantitative, the data production employs randomization, and the population
distribution is approximately normal.
State the null and alternative hypothesis.
A. H 0 : the population mean is zero. H a : the population mean is negative.
B. H 0 : the population mean is zero. H a : the population mean is positive.
C. H 0 : the population mean is positive. H a : the population mean is zero.
D. H 0 : the population mean is zero. H a : the population mean is not zero.
Find the test statistic from the given table.
t=
(Round to three decimal places as needed.)
Find the P-value
(Round to three decimal places as needed.)
State the conclusion of this study.
A. No conclusion can be drawn from this study.
B. There is evidence that the coupons led to higher sales than did the outside posters.
C. There is no evidence that the coupons led to higher sales than did the outside posters.
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Online 16 - Section 9.3-Doug Ensley
4. When 195 workers aged 18-25 were asked how many hours they worked in the previous week, the mean was 37.64 with a
standard deviation of 13.66. Does this suggest that the population mean work week for this age group differs from 40
hours? Answer by completing parts a through d.
a. Identify the relevant and parameter variable. Choose the correct relevant variable below.
A. The relevant variable is the population mean work week (in hours) for workers aged 18-25.
B. The relevant variable is the 195 workers.
C. The relevant variable is the number of hours worked in the previous week by workers aged
18-25.
D. The relevant variable is the maximum number of hours worked in a week.
Identify the parameter. Choose the correct parameter below.
A. The parameter of interest is the population mean work week (in hours) for workers aged 18-25.
B. The parameter of interest is the 195 workers.
C. The parameter of interest is the number of hours worked in the previous week by workers aged
18-25.
D. The parameter of interest is the maximum number of hours worked in a week.
b. State the null and alternative hypotheses.
State the null hypothesis. Choose the correct answer below.
A. H 0 : μ ≠ 40
B. H 0 : μ > 40
C. H 0 : μ < 40
D. H 0 : μ = 40
State the alternative hypothesis. Choose the correct answer below.
A. H a : μ ≠ 40
B. H a : μ = 40
C. H a : μ > 40
D. H a : μ < 40
c. Find the test statistic value.
t=
(Round to two decimal places as needed.)
Interpret the test statistic value. Choose the correct answer below.
A. The sample mean is 2.41 standard errors below the mean hypothesized in the null hypothesis.
B. The sample mean is 2.41 standard errors below the mean hypothesized in the alternative
hypothesis.
C. The sample mean is 2.41 standard errors above the mean hypothesized in the alternative
hypothesis.
D. The sample mean is 2.41 standard errors above the mean hypothesized in the null hypothesis.
d. Report the P-value and state the conclusion in context.
6 of 9 Report the P-value.
Online 16 - Section 9.3-Doug Ensley
P-value =
(Round to three decimal places as needed.)
State the conclusion in context. Use a significance level of 0.05. Choose the correct answer below.
A. The P-value is greater than the significance level so do not reject the null hypothesis. There is
not significant evidence that the population mean work week differs from 40 hours.
B. The P-value is less than the significance level so do not reject the null hypothesis. There is not
significant evidence that the population mean work week differs from 40 hours.
C. The P-value is greater than the significance level so reject the null hypothesis. There is
significant evidence that the population mean work week differs from 40 hours.
D. The P-value is less than the significance level so reject the null hypothesis. There is significant
evidence that the population mean work week differs from 40 hours.
5. In an experiment with 10 pairs of stores, the difference in the month's increased sales between the store that used coupons
and the store with the outside poster had a mean of $2814. Use the output shown to test that the population mean
difference is 0, carrying out the five steps of a significance test. Make a decision using a 0.05 significance level.
Test of mu = 0 vs. mu ≠ 0
Variable
N
Mean
StDev SE
Sales
10
2814
4142 1309.82
Variable
95.0% CI
T
P
Sales
(2809.1,2818.9) 2.148 0.06023
State the assumptions for a significance test of a population mean.
A. The variable is categorical, the data production employs randomization, and the population
distribution is approximately normal.
B. The variable is quantitative, and the population distribution is approximately normal.
C. The variable is quantitative, the data production employs randomization, and the population
distribution is approximately normal.
State the null and alternative hypothesis.
A. H 0 : the population mean is zero. H a : the population mean is not zero.
B. H 0 : the population mean is zero. H a : the population mean is positive.
C. H 0 : the population mean is zero. H a : the population mean is negative.
D. H 0 : the population mean is positive. H a : the population mean is zero.
Find the test statistic from the given table.
t=
(Round to three decimal places as needed.)
Find the P-value
(Round to three decimal places as needed.)
State the conclusion of this study.
A. There is no evidence that the coupons led to higher sales than did the outside posters.
B. No conclusion can be drawn from this study.
C. There is evidence that the coupons led to higher sales than did the outside posters.
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Online 16 - Section 9.3-Doug Ensley
1.
B. The relevant variable is the number of hours worked in the previous week by male workers.
A. The parameter of interest is the population mean work week (in hours) for men.
D. H 0 : μ = 40
D. H a : μ > 40
0
D.
The P-value is the probability of obtaining a sample with a mean of 45.7 or more hours assuming the null hypothesis were
true.
A.
Since the P-value is less than the significance level of 0.01, there is sufficient evidence to reject the null hypothesis and to
conclude that the population mean work week for men exceeds 40 hours.
2.
D. The relevant variable is the number of hours worked in the previous week by workers aged 18-25.
A. The parameter of interest is the population mean work week (in hours) for workers aged 18-25.
A. H 0 : μ = 40
A. H a : μ ≠ 40
− 2.29
C. The sample mean is 2.29 standard errors below the mean hypothesized in the null hypothesis.
0.023
B.
The P-value is less than the significance level so reject the null hypothesis. There is significant evidence that the population
mean work week differs from 40 hours.
3.
C.
The variable is quantitative, the data production employs randomization, and the population distribution is approximately
normal.
D. H 0 : the population mean is zero. H a : the population mean is not zero.
2.518
0.033
B. There is evidence that the coupons led to higher sales than did the outside posters.
4.
C. The relevant variable is the number of hours worked in the previous week by workers aged 18-25.
A. The parameter of interest is the population mean work week (in hours) for workers aged 18-25.
D. H 0 : μ = 40
A. H a : μ ≠ 40
− 2.41
A. The sample mean is 2.41 standard errors below the mean hypothesized in the null hypothesis.
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0.017
Online 16 - Section 9.3-Doug Ensley
D.
The P-value is less than the significance level so reject the null hypothesis. There is significant evidence that the population
mean work week differs from 40 hours.
5.
C.
The variable is quantitative, the data production employs randomization, and the population distribution is approximately
normal.
A. H 0 : the population mean is zero. H a : the population mean is not zero.
2.148
0.060
A. There is no evidence that the coupons led to higher sales than did the outside posters.
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