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Homework #7 (Sections 4.2 part 2 & 4.4)-Dayja Melton
2. An engineer wants to determine how the weight of a gas-powered car, x, affects gas mileage, y. The accompanying data
represent the weights of various domestic cars and their miles per gallon in the city for the most recent model year.
Complete parts (a) through (d) below.
1
Click here to view the weight and gas mileage data.
(a) Find the least-squares regression line treating weight as the explanatory variable and miles per gallon as the response
variable.
y=
x+
(Round the x coefficient to five decimal places as needed. Round the constant to two decimal places as needed.)
(b) Interpret the slope and y-intercept, if appropriate. Choose the correct answer below and fill in any answer boxes in your
choice.
(Use the answer from part a to find this answer.)
A. For every pound added to the weight of the car, gas mileage in the city will decrease by
mile(s) per gallon, on average. A weightless car will get
miles
per gallon, on average.
B. For every pound added to the weight of the car, gas mileage in the city will decrease by
mile(s) per gallon, on average. It is not appropriate to interpret the y-intercept.
C. A weightless car will get
interpret the slope.
miles per gallon, on average. It is not appropriate to
D. It is not appropriate to interpret the slope or the y-intercept.
(c) A certain gas-powered car weighs 3700 pounds and gets 20 miles per gallon. Is the miles per gallon of this car above
average or below average for cars of this weight?
Below
Above
(d) Would it be reasonable to use the least-squares regression line to predict the miles per gallon of a hybrid gas and
electric car? Why or why not?
A. Yes, because the hybrid is partially powered by gas.
B. No, because the absolute value of the correlation coefficient is less than the critical value for a
sample size of n = 11.
C. Yes, because the absolute value of the correlation coefficient is greater than the critical value
for a sample size of n = 11.
D. No, because the hybrid is a different type of car.
1: Car Weight and MPG
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Homework #7 (Sections 4.2 part 2 & 4.4)-Dayja Melton
Weight
(pounds), x
Miles per
Gallon, y
3754
17
3960
16
2760
24
3511
20
3377
21
2978
23
3641
18
2525
24
3530
19
3793
18
3261
18
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Homework #7 (Sections 4.2 part 2 & 4.4)-Dayja Melton
3. The accompanying data represent the number of days absent, x, and the final exam score, y, for a sample of college
students in a general education course at a large state university. Complete parts (a) through (e) below.
2
Click the icon to view the absence count and final exam score data.
3
Click the icon to view a table of critical values for the correlation coefficient.
(a) Find the least-squares regression line treating number of absences as the explanatory variable and the final exam score
as the response variable.
y=
x+
(Round to three decimal places as needed.)
(b) Interpret the slope and the y-intercept, if appropriate. Choose the correct answer below and fill in any answer boxes in
your choice.
(Round to three decimal places as needed.)
A. For every additional absence, a student's final exam score drops
average. It is not appropriate to interpret the y-intercept.
points, on
B. The average final exam score of students who miss no classes is
appropriate to interpret the slope.
. It is not
C. For every additional absence, a student's final exam score drops
points, on
average. The average final exam score of students who miss no classes is
.
D. It is not appropriate to interpret the slope or the y-intercept.
(c) Predict the final exam score for a student who misses five class periods.
y=
(Round to two decimal places as needed.)
Compute the residual.
(Round to two decimal places as needed.)
Is the final exam score above or below average for this number of absences?
Below
Above
(d) Draw the least-squares regression line on the scatter diagram of the data. Choose the correct graph below.
B.
Final Exam Score
Exam Scores vs. Absences
100
80
60
40
20
0
2
4
6
8
Exam Scores vs. Absences
Final Exam Score
A.
10
100
80
60
40
20
0
2
Number of Absences
D.
Final Exam Score
Exam Scores vs. Absences
100
80
60
40
20
0
2
4
6
6
8
10
8
10
Exam Scores vs. Absences
Final Exam Score
C.
4
Number of Absences
100
80
60
40
20
0
Number of Absences
2
4
6
8
10
Number of Absences
(e) Would it be reasonable to use the least-squares regression line to predict the final exam score for a student who has
missed 15 class periods? Why or why not?
A. No, because 15 absences is outside the scope of the model.
B. No, because the absolute value of the correlation coefficient is less than the critical value for a
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Homework #7 (Sections 4.2 part 2 & 4.4)-Dayja Melton
sample size of n = 10.
C. Yes, because the absolute value of the correlation coefficient is greater than the critical value
for a sample size of n = 10.
D. Yes, because the purpose of finding the regression line is to make predictions outside the
scope of the model.
2: Absences and Final Exam Scores
No. of
absences, x
0
Final
exam score, y 89.1
1
2
3
4
5
6
7
8
9
85.5
83.3
80.3
78.9
74.6
63.5
71.6
65.9
66.2
3: Critical Values for Correlation Coefficient
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Homework #7 (Sections 4.2 part 2 & 4.4)-Dayja Melton
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Homework #7 (Sections 4.2 part 2 & 4.4)-Dayja Melton
4. What is meant by a marginal distribution? What is meant by a conditional distribution?
What is meant by a marginal distribution?
A. A marginal distribution is a frequency or relative frequency distribution of either the row or
column variable in a contingency table.
B. A marginal distribution is the relative frequency of each category of one variable, given a
specific value of the other variable in a contingency table.
C. A marginal distribution is the effect of either row variable or the column variable in the
contingency table.
D. A marginal distribution is the relative distribution of both row or column variables in the
contingency table.
What is meant by a conditional distribution?
A. A conditional distribution is the relative association between two categorical variables in the
contingency table.
B. A conditional distribution is a frequency or relative frequency distribution of either the row or
column variable in a contingency table.
C. A conditional distribution is the relative distribution of both row or column variables in the
contingency table.
D. A conditional distribution lists the relative frequency of each category of the response variable,
given a specific value of the explanatory variable in a contingency table.
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Homework #7 (Sections 4.2 part 2 & 4.4)-Dayja Melton
5. Consider the data set given in the accompanying table. Complete parts (a) through (d).
4
Click the icon to view the data table.
(a) Construct a frequency marginal distribution.
x1
x2
x3
y1
20
15
50
y2
30
15
50
Marginal
distribution
Marginal
distribution
(b) Construct a relative frequency marginal distribution.
x1
x2
x3
y1
20
15
50
y2
30
15
50
Relative frequency
marginal distribution
Relative frequency
marginal distribution
(Round to three decimal places as needed.)
1
(c) Construct a conditional distribution by x.
x1
x2
x3
1
1
1
y1
y2
Total
(d) Draw a bar graph of the conditional distribution found in part (c). Let the blue (left) bars represent the conditional
distribution of y1 and let the red (right) bars represent the conditional distribution of y2 . Choose the correct graph below.
B.
0.8
0.6
0.4
0.2
0
x1
x2
x3
C.
1
Relative Frequency
1
Relative Frequency
Relative Frequency
A.
0.8
0.6
0.4
0.2
0
x1
x2
x3
1
0.8
0.6
0.4
0.2
0
x1
x2
x3
4: Data Table
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x1
x2
x3
y1
20
15
50
y2
30
15
50
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Homework #7 (Sections 4.2 part 2 & 4.4)-Dayja Melton
6. In an effort to gauge how the country's population feels about the immigration, researchers surveyed adult citizens. One
question asked was, "On the whole, do you think immigration is a good thing or a bad thing for this country today?" The
results of the survey, by ethnicity, are given in the acompanying table. Complete parts (a) through (f).
5
Click the icon to view the data table.
(a) How many adult citizens were surveyed?
How many Hispanics were surveyed?
(b) Construct a relative frequency marginal distribution.
Ethnicity
Non-Hispanic
Whites
Blacks
Hispanics
Good thing
180
154
147
Bad thing
110
101
33
Good and bad
9
14
12
No opinion
9
11
6
Opinion
Relative frequency
marginal
distribution
Relative frequency
marginal
distribution
(Round to three decimal places as needed.)
1
(c) What proportion of adult citizens feel that immigration is a good thing for this country?
(Round to three decimal places as needed.)
(d) Construct a conditional distribution of immigration opinion by ethnicity.
Ethnicity
Opinion
Non-Hispanic
Whites
Blacks
Hispanics
Good thing
Bad thing
Good and bad
No opinion
Total
1
(Round to three decimal places as needed.)
1
1
(e) Draw a bar graph of the conditional distribution found in part (d). Let the left-most (blue) bars represent "Good thing"
opinion, the middle-left (green) bars represent "Bad thing" opinion, the middle-right (red) bars represent the "Good and bad"
opinion, and the right-most (gray) bars represent "No opinion". Choose the correct graph below.
A.
B.
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C.
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Homework #7 (Sections 4.2 part 2 & 4.4)-Dayja Melton
1
1
1
0.8
0.8
0.8
(f) Is ethnicity associated with opinion regarding immigration? If so, how? Choose the correct answer below.
A. No, ethnicity is not associated with opinion regarding immigration.
B. Yes, ethnicity is associated with opinion regarding immigration. Hispanics are more likely to
feel that immigration is a good thing for the country and much less likely to feel it is a bad
thing.
C. Yes, ethnicity is associated with opinion regarding immigration. Hispanics are more likely to
feel that immigration is a bad thing for the country and much less likely to feel it is a good
thing.
5: Data Table
Non-Hispanic
Whites
Blacks
Hispanics
Good thing
180
154
147
Bad thing
110
101
33
Good and bad
9
14
12
No opinion
9
11
6
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Homework #7 (Sections 4.2 part 2 & 4.4)-Dayja Melton
7. Is there an association between party affiliation and gender? The accompanying data represent the gender and party
affiliation of registered voters based on a random sample of 810 adults. Complete parts (a) through (f).
6
Click the icon to view the data table.
(a) Construct a frequency marginal distribution.
Gender
Political Party
Female
Male
Republican
110
120
Democrat
150
101
Independent
150
179
Frequency Marginal
Distribution for Gender
Frequency Marginal
Distribution for Political
Party
(b) Construct a relative frequency marginal distribution.
Gender
Political Party
Female
Male
Republican
110
120
Democrat
150
101
Independent
150
179
Relative frequency
marginal distribution
Relative frequency
marginal distribution
(Round to three decimal places as needed.)
1
(c) What proportion of registered voters considers themselves to be Independent?
(Round to three decimal places as needed.)
(d) Construct a conditional distribution of party affiliation by gender.
Gender
Political Party
Female
Male
Republican
Democrat
Independent
Total
1
1
(Round to three decimal places as needed.)
(e) Draw a bar graph of the conditional distribution found in part (d). Let the red bars (left most) represent Republican, the
blue bars (middle) represent Democrat, and the green bars (right most) represent Independent. Choose the correct graph
below.
A.
B.
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C.
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Homework #7 (Sections 4.2 part 2 & 4.4)-Dayja Melton
(f) Is gender associated with party affiliation? If so, how? Choose the correct answer below.
A. Yes, gender is associated with party affiliation. Males are more likely to be Independents and
less likely to be Democrats.
B. Yes, gender is associated with party affiliation. Males are more likely to be Independents and
less likely to be Republicans.
C. No, gender is not associated with party affiliation.
6: More Info
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Female
Male
Republican
110
120
Democrat
150
101
Independent
150
179
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