Question
11. Urban traffic congestion throughout the world has been increasing in recent years, especially in developing countries. The accompanying table shows the number of minutes
11. Urban traffic congestion throughout the world has been increasing in recent years, especially in developing countries. The accompanying table shows the number of minutes that randomly selected drivers spend stuck in traffic in various cities on both weekdays and weekends. Complete parts a through e below.
| City A
| City B
| City C
| City D
| |
| Weekday
| 94
| 41
| 54
| 55
|
| 76
| 112
| 83
| 70
| |
| 122
| 67
| 80
| 39
| |
| 74
| 73
| 98
| 48
| |
| 93
| 97
| 120
| 50
| |
| Weekend
| 82
| 82
| 34
| 30
|
| 86
| 26
| 87
| 44
| |
| 73
| 105
| 72
| 43
| |
| 76
| 81
| 64
| 44
| |
| 59
| 76
| 36
| 42
|
a)Using =0.05, is there significant interaction between the city and time of the week? Identify the hypotheses for the interaction between the city and time of the week. Choose the correct answer below.
A.
H0:
City=Time,
H1:
CityTime
B.
H0:
CityTime,
H1:
City=Time
C.
H0:
City and time of the week do not interact,
H1:
City and time of the week do interact
D.
H0:
City and time of the week do interact,
H1:
City and time of the week do not interact
Find the p-value for the interaction between city and time of the week.
p-value=
(Round to three decimal places as needed.)
Draw the appropriate conclusion for the interaction between the city and time of the week. Choose the correct answer below.
A.
Reject the null hypothesis. There is insufficient evidence to conclude that the means differ.
B.
Do not reject the null hypothesis. There is insufficient evidence to conclude that the city and time of the week interact.
C.
Reject the null hypothesis. There is sufficient evidence to conclude that the city and time of the week interact.
D.
Do not reject the null hypothesis. There is insufficient evidence to conclude that the means differ.
b)Using two-way ANOVA and =0.05, does the city have an effect on the amount of time stuck in traffic? Identify the hypotheses to test for the effect of the city. Choose the correct answer below.
A.
H0:
City=Time,
H1:
CityTime
B.
H0:
City A=City B=City C=City D,
H1:
Not all city means are equal
C.
H0:
City ACity BCity CCity D,
H1:
City A=City B=City C=City D
D.
H0:
City A=City B=City C=City D,
H1:
City A>City B>City C>City D
Find the p-value for the effect of the city.
p-value=
(Round to three decimal places as needed.)
Draw the appropriate conclusion for the effect of the city. Choose the correct answer below.
A.
Reject the null hypothesis. There is sufficient evidence to conclude that not all city means are equal.
B.
Do not reject the null hypothesis. There is sufficient evidence to conclude that the means differ.
C.
Do not reject the null hypothesis. There is insufficient evidence to conclude that not all city means are equal.
D.
It is inappropriate to analyze because the city and the time of the week interact.
c)Using two-way ANOVA and =0.05, does the time of the week have an effect on the amount of time stuck in traffic? Identify the hypotheses to test for the effect of the time of the week. Choose the correct answer below.
A.
H0:
City=Time,
H1:CityTime
B.
H0:
Weekday=Weekend,
H1:
Not all time of the week means are equal
C.
H0:
WeekdayWeekend,
H1:
Weekday=Weekend
D.
H0:
City A=City B=City C=City D,
H1:
Not all time of the week means are equal
Find the p-value for the effect of the time of the week.
p-value=
(Round to three decimal places as needed.)
Draw the appropriate conclusion for the effect of the time of the week. Choose the correct answer below.
A.
Do not reject the null hypothesis. There is sufficient evidence to conclude that the means differ.
B.
Reject the null hypothesis. There is sufficient evidence to conclude that not all time of the week means are equal.
C.
Do not reject the null hypothesis. There is insufficient evidence to conclude that not all time of the week means are equal.
D.
It is inappropriate to analyze because the city and the time of the week interact.
d)If warranted, determine which means are significantly different using =0.05.
Are the means for City A and City B significantly different?
A.
No
B.
Yes
C.
The comparison is unwarranted because there is insufficient evidence to conclude that not all city means are equal.
D.
The comparison is unwarranted because the city and the time of the week interact.
Are the means for City A and City C significantly different?
A.
No
B.
Yes
C.
The comparison is unwarranted because there is insufficient evidence to conclude that not all city means are equal.
D.
The comparison is unwarranted because the city and the time of the week interact.
Are the means for City A and City D significantly different?
A.
No
B.
Yes
C.
The comparison is unwarranted because there is insufficient evidence to conclude that not all city means are equal.
D.
The comparison is unwarranted because the city and the time of the week interact.
Are the means for City B and City C significantly different?
A.
Yes
B.
No
C.
The comparison is unwarranted because there is insufficient evidence to conclude that not all city means are equal.
D.
The comparison is unwarranted because the city and the time of the week interact.
Are the means for City B and City D significantly different?
A.
Yes
B.
No
C.
The comparison is unwarranted because there is insufficient evidence to conclude that not all city means are equal.
D.
The comparison is unwarranted because the city and the time of the week interact.
Are the means for City C and City D significantly different?
A.
Yes
B.
No
C.
The comparison is unwarranted because there is insufficient evidence to conclude that not all city means are equal.
D.
The comparison is unwarranted because the city and the time of the week interact.
Are the means for weekdays and weekends significantly different?
A.
No, because there is insufficient evidence to conclude that not all time of the week means are equal.
B.
Yes, because there is sufficient evidence to conclude that not all time of the week means are equal.
C.
Yes, because there is insufficient evidence to conclude that not all time of the week means are equal.
D.
The comparison is unwarranted because the city and the time of the week interact.
e) Construct an interaction plot for the city and the time of the week.
12. The accompanying table shows the retirement ages for a random sample of retirees from four different countries according to their genders. Complete parts a through e below.
| Country A | Country B | Country C | Country D | |
| Women | 67 | 62 | 60 | 58 |
| 72 | 66 | 63 | 71 | |
| 77 | 76 | 55 | 48 | |
| 75 | 64 | 68 | 52 | |
| 64 | 64 | 59 | 55 | |
| 77 | 60 | 65 | 56 |
| Country A | Country B | Country C | Country D | |
| Men | 76 | 68 | 65 | 59 |
| 66 | 64 | 67 | 63 | |
| 80 | 67 | 56 | 59 | |
| 75 | 78 | 72 | 60 | |
| 72 | 69 | 68 | 66 | |
| 69 | 74 | 56 | 59 |
a)Using =0.01, is there significant interaction between the country and the gender ?Identify the hypotheses for the interaction between the country and the gender. Choose the correct answer below.
A.
H0:
C=G,
H1:
CG
B.
H0:
Country and gender do interact,
H1:
Country and gender do not interact
C.
H0:
Country and gender do not interact,
H1:
Country and gender do interact
D.
H0:
CG,
H1:
C=G
Find the p-value for the interaction between the country and the gender.
p-value=
(Round to three decimal places as needed.)
Draw the appropriate conclusion for the interaction between the country and the gender. Choose the correct answer below.
A.
Reject
the null hypothesis. There is insufficient evidence to conclude that the means differ.
B.
Do not reject
the null hypothesis. There is insufficient evidence to conclude that the country and the gender interact.
C.
Do not reject
the null hypothesis. There is insufficient evidence to conclude that the means differ.
D.
Reject
the null hypothesis. There is sufficient evidence to conclude that the country and the gender interact.
b)Using two-way ANOVA and =0.01, does the country have an effect on the retirement age? Identify the hypotheses to test for the effect of the country. Choose the correct answer below.
A.
H0:
A=B=C=D,
H1:
Not all country means are equal
B.
H0:
ABCD,
H1:
A=B=C=D
C.
H0:
C=G,
H1:
CG
D.
H0:
A=B=C=D,
H1:
A>B>C>D
Find the p-value for the effect of the country.
p-value=
(Round to three decimal places as needed.)
Draw the appropriate conclusion for the effect of the country. Choose the correct answer below.
A.
Do not reject
the null hypothesis. There is sufficient evidence to conclude that the means differ.
B.
Do not reject the null hypothesis. There is insufficient evidence to conclude that not all country means are equal.
C.
Reject
the null hypothesis. There is sufficient evidence to conclude that not all country means are equal.
D.
It is inappropriate to analyze because the country and the gender interact.
c)Using two-way ANOVA and =0.01, does the gender of the retiree have an effect on the retirement age? Identify the hypotheses to test for the effect of gender. Choose the correct answer below.
A.
H0:
W=M,
H1:
Not all gender means are equal
B.
H0:
A=B=C=D,
H1:
Not all gender means are equal
C.
H0:
WM,
H1:
W=M
D.
H0:
C=G,
H1:
CG
Find the p-value for the effect of gender.
p-value=
(Round to three decimal places as needed.)
Draw the appropriate conclusion for the effect of gender. Choose the correct answer below.
A.
Reject
the null hypothesis. There is insufficient evidence to conclude that the means differ.
B.
Do not reject
the null hypothesis. There is insufficient evidence to conclude that not all gender means are equal.
C.
It is inappropriate to analyze because the country and the gender interact.
D.
Reject
the null hypothesis. There is sufficient evidence to conclude that not all gender means are equal.
d)Using =0.01, if warranted, determine which means are significantly different. Are the means for Country A and Country B significantly different?
A.
Yes
B.
No
C.
The comparison is unwarranted because there is insufficient evidence to conclude that not all country means are equal.
D.
The comparison is unwarranted because the country and the gender interact.
Are the means for Country A and Country C significantly different?
A.
No
B.
Yes
C.
The comparison is unwarranted because there is insufficient evidence to conclude that not all country means are equal.
D.
The comparison is unwarranted because the country and the gender interact.
Are the means for Country A and Country D significantly different?
A.
Yes
B.
No
C.
The comparison is unwarranted because there is insufficient evidence to conclude that not all country means are equal.
D.
The comparison is unwarranted because the country and the gender interact.
Are the means for Country B and Country C significantly different?
A.
Yes
B.
No
C.
The comparison is unwarranted because there is insufficient evidence to conclude that not all country means are equal.
D.
The comparison is unwarranted because the country and the gender interact.
Are the means for Country B and Country D significantly different?
A.
No
B.
Yes
C.
The comparison is unwarranted because there is insufficient evidence to conclude that not all country means are equal.
D.
The comparison is unwarranted because the country and the gender interact.
Are the means for Country C and Country D significantly different?
A.
No
B.
Yes
C.
The comparison is unwarranted because there is insufficient evidence to conclude that not all country means are equal.
D.
The comparison is unwarranted because the country and the gender interact.
Are the means for women and men significantly different?
A.
No,
because there is insufficient evidence to conclude that not all gender means are equal.
B.
No, because there is sufficient evidence to conclude that not all gender means are equal.
C.
Yes,
because there is sufficient evidence to conclude that not all gender means are equal.
D.
The comparison is unwarranted because the country and the gender interact.
d)Using =0.01, if warranted, determine which means are significantly different. Are the means for Country A and Country B significantly different?
A.
Yes
B.
No
C.
The comparison is unwarranted because there is insufficient evidence to conclude that not all country means are equal.
D.
The comparison is unwarranted because the country and the gender interact.
Are the means for Country A and Country C significantly different?
A.
No
B.
Yes
C.
The comparison is unwarranted because there is insufficient evidence to conclude that not all country means are equal.
D.
The comparison is unwarranted because the country and the gender interact.
Are the means for Country A and Country D significantly different?
A.
Yes
B.
No
C.
The comparison is unwarranted because there is insufficient evidence to conclude that not all country means are equal.
D.
The comparison is unwarranted because the country and the gender interact.
Are the means for Country B and Country C significantly different?
A.
Yes
B.
No
C.
The comparison is unwarranted because there is insufficient evidence to conclude that not all country means are equal.
D.
The comparison is unwarranted because the country and the gender interact.
Are the means for Country B and Country D significantly different?
A.
No
B.
Yes
C.
The comparison is unwarranted because there is insufficient evidence to conclude that not all country means are equal.
D.
The comparison is unwarranted because the country and the gender interact.
Are the means for Country C and Country D significantly different?
A.
No
B.
Yes
C.
The comparison is unwarranted because there is insufficient evidence to conclude that not all country means are equal.
D.
The comparison is unwarranted because the country and the gender interact.
Are the means for women and men significantly different?
A.
No, because there is insufficient evidence to conclude that not all gender means are equal.
B.
No, because there is sufficient evidence to conclude that not all gender means are equal.
C.
Yes, because there is sufficient evidence to conclude that not all gender means are equal.
D.
The comparison is unwarranted because the country and the gender interact.
d)Using =0.01, if warranted, determine which means are significantly different.
Are the means for Country A and Country B significantly different?
A.
Yes
B.
No
C.
The comparison is unwarranted because there is insufficient evidence to conclude that not all country means are equal.
D.
The comparison is unwarranted because the country and the gender interact.
Are the means for Country A and Country C significantly different?
A.
No
B.
Yes
C.
The comparison is unwarranted because there is insufficient evidence to conclude that not all country means are equal.
D.
The comparison is unwarranted because the country and the gender interact.
Are the means for Country A and Country D significantly different?
A.
Yes
B.
No
C.
The comparison is unwarranted because there is insufficient evidence to conclude that not all country means are equal.
D.
The comparison is unwarranted because the country and the gender interact.
Are the means for Country B and Country C significantly different?
A.
Yes
B.
No
C.
The comparison is unwarranted because there is insufficient evidence to conclude that not all country means are equal.
D.
The comparison is unwarranted because the country and the gender interact.
Are the means for Country B and Country D significantly different?
A.
No
B.
Yes
C.
The comparison is unwarranted because there is insufficient evidence to conclude that not all country means are equal.
D.
The comparison is unwarranted because the country and the gender interact.
Are the means for Country C and Country D significantly different?
A.
No
B.
Yes
C.
The comparison is unwarranted because there is insufficient evidence to conclude that not all country means are equal.
D.
The comparison is unwarranted because the country and the gender interact.
Are the means for women and men significantly different?
A.
No, because there is insufficient evidence to conclude that not all gender means are equal.
B.
No, because there is sufficient evidence to conclude that not all gender means are equal.
C.
Yes, because there is sufficient evidence to conclude that not all gender means are equal.
D.
The comparison is unwarranted because the country and the gender interact.
e) Construct an interaction plot for country and gender.
13. Television advertisers base their investment decisions regarding the promotion of their products and services on demographic information about television viewers. The age of the viewers is a key factor in this process. The accompanying table shows the number of hours that a random sample of individuals watched television during the week. The individuals are grouped according to their ages. Complete parts a and b.
USE range for a=0.05
| 18-24 | 25-34 | 35-49 | 50-64 |
| 38 | 41 | 43 | 51 |
| 15 | 37 | 19 | 39 |
| 17 | 32 | 25 | 40 |
| 14 | 36 | 36 | 32 |
| 16 | 21 | 47 | 72 |
a. Perform a one-way ANOVA using =0.05 to determine if there is a difference in the average number of hours per week of television viewing by the four age groups.
A.
H0:
1=2=3=4
H1:
1234
B.
H0:
Not all the means are equal.
H1:
1=2=3=4
C.
H0:
1234
H1:
1=2=3=4
D.
H0:
1=2=3=4
H1:
Not all the means are equal.
Complete the ANOVA summary table below.
| Source
| Sum of Squares
| Degrees of Freedom
| Mean Sum of Squares
| F
|
| Between
| enter your response here
| enter your response here
| enter your response here
| enter your response here
|
| Within
| enter your response here
| enter your response here
| enter your response here
| |
| Total
| enter your response here
| enter your response here
|
(Round to three decimal places as needed.)Determine the p-value for this test.
p-value=enter your response here
(Round to three decimal places as needed.)
State the conclusion for=0.05.
Since the p-value is(less, greater) than the level of significance,(reject, do not reject) the null hypothesis and conclude that there (is, is not) a difference in the average number of hours per week of television viewing by the four age groups.
b. If warranted, perform a multiple comparison test to determine which pairs are different using =0.05.
Select the correct choice and, if necessary, fill in the answer box to complete your choice.
A.
The Tukey-Kramer critical range for equal sample sizes is
CR=enter your response here.
(Round to two decimal places as needed.)
B.
Since the null hypothesis in part a was rejected, multiple comparison tests are not warranted for these data.
C.
Since the null hypothesis in part a was not rejected, multiple comparison tests are not warranted for these data.
Determine the ranges for which the Tukey-Kramer test shows sufficient evidence to conclude that the means of those ranges are different.
For the 18-24 versus 25-34 age ranges,
(the means are not significantly different.
a multiple comparison test was not warranted.
the means are significantly different.)
For the 18-24 versus 35-49 age ranges,
(the means are not significantly different.
a multiple comparison test was not warranted.
the means are significantly different.)
For the 18-24 versus 50-64 age ranges,
(the means are significantly different.
a multiple comparison test was not warranted.
the means are not significantly different.)
For the 25-34 versus 35-49 age ranges,
(a multiple comparison test was not warranted.
the means are significantly different.
the means are not significantly different.)
For the 25-34 versus 50-64 age ranges,
(a multiple comparison test was not warranted.
the means are not significantly different.
the means are significantly different.)
For the 35-49 versus 50-64 age ranges,
(the means are not significantly different.
a multiple comparison test was not warranted.
the means are significantly different.)
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Essentials Of College Algebra
Authors: Margaret L Lial, John E Hornsby, David I Schneider, Teresa McGinnis
10th Edition
0321970632, 9780321970633
