# Probability in Voter Registration

Question 1 (5 points)

A review of voter registration records in a small town yielded the following table of the number of males and females registered as Democrat, Republican, or some other affiliation.

Male Female

Democrat 300 600

Republican 500 300

Other 200 100

What proportion of registered voters are Democrats?

a. 30%

b. 45%

c. 60%

d. 100%

_________________________________________________

Question 2 (5 points)

A review of voter registration records in a small town yielded the following table of the number of males and females registered as Democrat, Republican, or some other affiliation.

Male Female

Democrat 300 600

Republican 500 300

Other 200 100

What proportion of male voters are registered as Republicans?

a. 100%

b. 75%

c. 50%

d. 25%

_________________________________________________

Question 3 (5 points)

A review of voter registration records in a small town yielded the following table of the number of males and females registered as Democrat, Republican, or some other affiliation.

Male Female

Democrat 300 600

Republican 500 300

Other 200 100

What proportion of the registered Democrats are female voters?

a. 15%

b. 33.3%

c. 66.7%

d. 100%

_________________________________________________

Question 4 (5 points)

Male Female

Democrat 300 600

Republican 500 300

Other 200 100

What proportion of registered female voters are Republicans?

a. 15%

b. 30%

c. 60%

d. 100%

_________________________________________________

Question 5 (5 points)

In a study of heart disease in male federal employees, researchers classified 356 volunteer subjects according to their socioeconomic status (SES) and their smoking habits. There are three categories of SES: high, middle, and low. The subjects were asked whether they were current smokers, former smokers, or had never smoked. The following table summarizes the data.

Smoking High Middle Low Total

Current 51 22 43 116

Former 92 21 28 141

Never 68 9 22 99

Total 211 52 93 356

What is the calculated Chi-square for this study reounded to two (2) decimal places?

a. 4.58

b. 18.51

c. 68.75

d. insufficient information to calculate.

_________________________________________________

Question 6 (10 points)

Even though Puerto Rico is a territory of the United States there are many cultural differences between the states on the continent and the island of Puerto Rico. These differences include the way consumers handle problems with purchases. Two researchers surveyed owners of VCRs in the Northeast U.S. and in Puerto Rico. They asked those who had experienced problems with their VCRs whether they complained. The results are given in the table below.

Complaints States Puerto Rico Totals

NO 94 33 127

YES 330 64 394

Totals 424 97 521

Test the hypothesis that the proportion of VCR consumers who complain is the same in the continental U.S as it is in Puerto Rico.

Based on you test, the null hypothesis should be:

a. accepted.

b. rejected.

c. studied further.

d. thrown out.

_________________________________________________

Question 7 (10 points)

Even though Puerto Rico is a territory of the United States there are many cultural differences between the states on the continent and the island of Puerto Rico. These differences include the way consumers handle problems with purchases. Two researchers surveyed owners of VCRs in the Northeast U.S. and in Puerto Rico. They asked those who had experienced problems with their VCRs whether they complained. The results are given in the table below.

Complaints States Puerto Rico Totals

NO 94 33 127

YES 330 64 394

Totals 424 97 521

At what probability, rounded to four decimal places, does the difference in number of complaints between continental U.S. and Puerto Rician VCR owners change significance?

a. 0.0050

b. 0.0142

c. 0.0284

d. 0.0500

_________________________________________________

Question 8 (5 points)

An experiment was conducted to compare the results of four different treatments, A, B, C, and D to patients suffering from agorophobia. The patients were divided into three different age groups and the four treatments administered to each group. After 24 weeks of treatment the patients were evaluated through a series of psychological tests. The number of individuals in each group that showed an improvement are listed for each treatment in the table below.

Group A B C D

1 6 10 8 9

2 4 9 5 7

3 12 15 14 14

Perform an analysis of variance (ANOVA). What is the F-value from your analysis rounded to two (2) decimal places?

a. 0.005

b. 0.55

c. 19.22

d. 25.58

_________________________________________________

Question 9 (10 points)

In the course of a clinical trial of measures to prevent coronary heart disease, blood pressure measurements were taken on 12,866 men. Individuals were classified by age group and race. The means for systolic blood pressure are given in the following table. (Data from W. M. Smith et al., "The multiple risk factor intervention trial," in H. M. Perry Jr., and W. M. Smith (eds.) Mild Hypertension: To Treat or Not to Treat, New York academy of Sciences, 1978, pp. 293-308.)

35-39 40-44 45-49 50-54 55-59

White 131.0 132.3 135.2 139.4 142.0

Nonwhite 132.3 134.2 137.2 141.3 144.1

Perform an analysis of variance (ANOVA). What is the p-value from your test.

a. 0.0005

b. 0.3712

c. 0.5592

d. 0.6603

_________________________________________________

Question 10 (10 points)

An experiment was conducted to compare the results of four different treatments, A, B, C, and D to patients suffering from agorophobia. The patients were divided into three different age groups and the four treatments administered to each group. After 24 weeks of treatment the patients were evaluated through a series of psychological tests. The number of individuals in each group that showed an improvement are listed for each treatment in the table below.

Group A B C D

1 6 10 8 9

2 4 9 5 7

3 12 15 14 14

Based on your analysis of variance (ANOVA) can one conclude that the four treatments produce equal results?

a. Yes

b. No

c. Sometimes

d. Never

_________________________________________________

Question 11 (10 points)

The number of salespersons employed by an automobile dealership has varied from a low of four to a high of eight. How does the number of new cars sold (Y) depend on the number of salespersons (X)? The sales manager examined sales records and located eight weeks during which no special incentive programs were employed. The data are shown in the table below.

Variables Cars sold(Y) Salespersons(X)

1 10 5

2 20 6

3 15 5

4 10 4

5 22 7

6 18 6

7 13 5

8 25 8

Using appropriate linear regression methodologies, the least-squares line for the data is:

I. y-hat = -7 + 4.108696X

II. y-hat = 2.111175 + 0.218877X

a. I only

b. II only

c. both I and II

d. neither I nor II

_________________________________________________

Question 12 (10 points)

The number of salespersons employed by an automobile dealership has varied from a low of four to a high of eight. How does the number of new cars sold (Y) depend on the number of salespersons (X)? The sales manager examined sales records and located eight weeks during which no special incentive programs were employed. The data are shown in the table below.

Variables Cars sold(Y) Salespersons(X)

1 10 5

2 20 6

3 15 5

4 10 4

5 22 7

6 18 6

7 13 5

8 25 8

Perform a hypothesis test to determine if the slope of the regression line is zero (0).

Based on your test, the hypothesis that the slope of the regression line is zero (0) would be:

a. accepted.

b. rejected

c. considered inconclusive.

d. considered insignificant.

_________________________________________________

Question 13 (10 points)

The number of salespersons employed by an automobile dealership has varied from a low of four to a high of eight. How does the number of new cars sold (Y) depend on the number of salespersons (X)? The sales manager examined sales records and located eight weeks during which no special incentive programs were employed. The data are shown in the table below.

Variables Cars sold(Y) Salespersons(X)

1 10 5

2 20 6

3 15 5

4 10 4

5 22 7

6 18 6

7 13 5

8 25 8

Using the formula for the regression (least-squares) line, predict the average number of new cars that would be sold if the number of salespersons employed for the week is six (6).

a. 3.42 cars

b. 12.89 cars

c. 17.65 cars

d. 37.89 cars

__________________________________________________

Short answer question

Homework Assignment 16

To study the effect of hematodes (microscopic worms) on plant growth an OSU botanist prepared 16 identical planting pots. A different number of hematodes was introduced into each pot. In each pot a tomato seedling was planted and its height measured (in centimeters) after 16 weeks. The results were:

Hematodes 1 2 3 4

0 10.8 9.1 13.5 9.2

1,000 11.1 11.1 8.2 11.3

5,000 5.4 4.6 7.4 5.0

10,000 5.4 4.6 7.4 5.0

1. What is the F-value from the test?

2. What is the p-value from the test?

3. From the test results your conclusion is. . . ?

Use your TI-83/83 Plus calculator. Clicking on the "Statistical Functions of TI-83/+" on main page, and selecting "Comparing Three or More Population Means: Analysis of Variance (ANOVA)" can find specific instructions on the operation of the calculator.

#### Solution Summary

Male Female

Democrat 300 600

Republican 500 300

Other 200 100

What proportion of registered voters are Democrats?

a. 30%

b. 45%

c. 60%

d. 100%

_________________________________________________

Question 2 (5 points)

Male Female

Democrat 300 600

Republican 500 300

Other 200 100

What proportion of male voters are registered as Republicans?

a. 100%

b. 75%

c. 50%

d. 25%

_________________________________________________

Question 3 (5 points)

Male Female

Democrat 300 600

Republican 500 300

Other 200 100

What proportion of the registered Democrats are female voters?

a. 15%

b. 33.3%

c. 66.7%

d. 100%

_________________________________________________

Question 4 (5 points)

Male Female

Democrat 300 600

Republican 500 300

Other 200 100

What proportion of registered female voters are Republicans?

a. 15%

b. 30%

c. 60%

d. 100%

_________________________________________________

Question 5 (5 points)

In a study of heart disease in male federal employees, researchers classified 356 volunteer subjects according to their socioeconomic status (SES) and their smoking habits. There are three categories of SES: high, middle, and low. The subjects were asked whether they were current smokers, former smokers, or had never smoked. The following table summarizes the data.

Smoking High Middle Low Total

Current 51 22 43 116

Former 92 21 28 141

Never 68 9 22 99

Total 211 52 93 356

What is the calculated Chi-square for this study reounded to two (2) decimal places?

a. 4.58

b. 18.51

c. 68.75

d. insufficient information to calculate.

_________________________________________________

Question 6 (10 points)

Even though Puerto Rico is a territory of the United States there are many cultural differences between the states on the continent and the island of Puerto Rico. These differences include the way consumers handle problems with purchases. Two researchers surveyed owners of VCRs in the Northeast U.S. and in Puerto Rico. They asked those who had experienced problems with their VCRs whether they complained. The results are given in the table below.

Complaints States Puerto Rico Totals

NO 94 33 127

YES 330 64 394

Totals 424 97 521

Test the hypothesis that the proportion of VCR consumers who complain is the same in the continental U.S as it is in Puerto Rico.

Based on you test, the null hypothesis should be:

a. accepted.

b. rejected.

c. studied further.

d. thrown out.

_________________________________________________

Question 7 (10 points)

Complaints States Puerto Rico Totals

NO 94 33 127

YES 330 64 394

Totals 424 97 521

At what probability, rounded to four decimal places, does the difference in number of complaints between continental U.S. and Puerto Rician VCR owners change significance?

a. 0.0050

b. 0.0142

c. 0.0284

d. 0.0500

_________________________________________________

Question 8 (5 points)

An experiment was conducted to compare the results of four different treatments, A, B, C, and D to patients suffering from agorophobia. The patients were divided into three different age groups and the four treatments administered to each group. After 24 weeks of treatment the patients were evaluated through a series of psychological tests. The number of individuals in each group that showed an improvement are listed for each treatment in the table below.

Group A B C D

1 6 10 8 9

2 4 9 5 7

3 12 15 14 14

Perform an analysis of variance (ANOVA). What is the F-value from your analysis rounded to two (2) decimal places?

a. 0.005

b. 0.55

c. 19.22

d. 25.58

_________________________________________________

Question 9 (10 points)

In the course of a clinical trial of measures to prevent coronary heart disease, blood pressure measurements were taken on 12,866 men. Individuals were classified by age group and race. The means for systolic blood pressure are given in the following table. (Data from W. M. Smith et al., "The multiple risk factor intervention trial," in H. M. Perry Jr., and W. M. Smith (eds.) Mild Hypertension: To Treat or Not to Treat, New York academy of Sciences, 1978, pp. 293-308.)

35-39 40-44 45-49 50-54 55-59

White 131.0 132.3 135.2 139.4 142.0

Nonwhite 132.3 134.2 137.2 141.3 144.1

Perform an analysis of variance (ANOVA). What is the p-value from your test.

a. 0.0005

b. 0.3712

c. 0.5592

d. 0.6603

_________________________________________________

Question 10 (10 points)

Group A B C D

1 6 10 8 9

2 4 9 5 7

3 12 15 14 14

Based on your analysis of variance (ANOVA) can one conclude that the four treatments produce equal results?

a. Yes

b. No

c. Sometimes

d. Never

_________________________________________________

Question 11 (10 points)

Variables Cars sold(Y) Salespersons(X)

1 10 5

2 20 6

3 15 5

4 10 4

5 22 7

6 18 6

7 13 5

8 25 8

Using appropriate linear regression methodologies, the least-squares line for the data is:

I. y-hat = -7 + 4.108696X

II. y-hat = 2.111175 + 0.218877X

a. I only

b. II only

c. both I and II

d. neither I nor II

_________________________________________________

Question 12 (10 points)

Variables Cars sold(Y) Salespersons(X)

1 10 5

2 20 6

3 15 5

4 10 4

5 22 7

6 18 6

7 13 5

8 25 8

Perform a hypothesis test to determine if the slope of the regression line is zero (0).

Based on your test, the hypothesis that the slope of the regression line is zero (0) would be:

a. accepted.

b. rejected

c. considered inconclusive.

d. considered insignificant.

_________________________________________________

Question 13 (10 points)

Variables Cars sold(Y) Salespersons(X)

1 10 5

2 20 6

3 15 5

4 10 4

5 22 7

6 18 6

7 13 5

8 25 8

Using the formula for the regression (least-squares) line, predict the average number of new cars that would be sold if the number of salespersons employed for the week is six (6).

a. 3.42 cars

b. 12.89 cars

c. 17.65 cars

d. 37.89 cars

__________________________________________________

Short answer question

Homework Assignment 16

To study the effect of hematodes (microscopic worms) on plant growth an OSU botanist prepared 16 identical planting pots. A different number of hematodes was introduced into each pot. In each pot a tomato seedling was planted and its height measured (in centimeters) after 16 weeks. The results were:

Hematodes 1 2 3 4

0 10.8 9.1 13.5 9.2

1,000 11.1 11.1 8.2 11.3

5,000 5.4 4.6 7.4 5.0

10,000 5.4 4.6 7.4 5.0

1. What is the F-value from the test?

2. What is the p-value from the test?

3. From the test results your conclusion is. . . ?

Use your TI-83/83 Plus calculator. Clicking on the "Statistical Functions of TI-83/+" on main page, and selecting "Comparing Three or More Population Means: Analysis of Variance (ANOVA)" can find specific instructions on the operation of the calculator.