A. P. Statistics Marginal and Conditional distributions. (Solutions)



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A.P. Statistics - Marginal and Conditional distributions. (Solutions)
Following are statistics from exit polls from the 2004 presidential election.





Bush

Kerry

Total

White Men

3049

1820

4869

White Women

3080

2464

5544

Non White Men

410

915

1325

Non-White Women

393

1229

1622

Total

6932

6428

13360

  1. Fill in the margins with the totals.

How many people were polled? 13,360

  1. What percent of white women voted for Kerry? 41.5%

  2. What percent of men voted for Bush? 46.4%


  1. Complete the chart to determine the marginal distribution of votes for each candidate in terms of percent.






Bush

Kerry













51.9%

48.1%







3.

Complete the chart to find the marginal distribution of gender in terms of percent.




























Male

Female










45.3%

54.7%










4. Complete the chart to find the conditional distribution of gender categories among Bush voters.








































White Men




White Women

Non-white Men

Non-white Women







44.0 %




44.4%







5.9%




4.9%














































Bush




Kerry




Total







No High School




268




273




541










HS Grad




1563




1412




2975










Some college




2360




2011




4371










College Grad




1847




1634




3481










Post Grad




962




1202




2164










Total




7000




6532




13532













5.

Find the margins with the totals.




























6.

Complete the chart to find the marginal distribution of education in terms of percent.





























































No HS

HS Grad

Some college




College grad




Post grad



















4.0%

22.0%

32.3%




25.7%







16.0%













7.

Complete the chart to find the conditional distribution of education among both Bush and Kerry voters.














































No HS

HS Grad

Some college




College grad

Post grad










Bush

3.8%

22.3%

33.7%




26.4%

13.7%













Kerry

4.2%

21.6%

30.8%




25.0%

18.4%






8. Illustrate # 7 in a back to back bar chart.








Bush

Kerry

Total

White Men

3049

1820

4869

White Women

3080

2464

5544

Non White Men

410

915

1325

Non-White Women

393

1229

1622

Total

6932

6428

13360




Bush

Kerry

Total




  1. Fill in the margins with the totals.

  2. What percent of voters were white, African-American, Latino, Asian, and other. Compare this with the data for 2000 on http://www.infoplease.com/ipa/A0762156.html. Did the pollsters interview a representative population?

  3. Complete the chart to find the conditional distribution of race among both Bush and Kerry voters.




White

Af-Amer

Latino

Asian

Other

Bush

87.5%

2.4%

6.9%

1.7%

1.6%

Kerry

66.2%

20.3%

8.9%

2.3%

2.3%




  1. Illustrate # 11 in a back to back bar chart.



  1. Write a paragraph describing you findings based on the previous data. Be sure to address marginal as well as conditional distributions.

14. Here are some statistics of the students at Wissahickon High School and their involvement in AP Courses.









Freshmen

Sophs

Juniors

Seniors




No AP Courses

311

296

277

133

1017

1

AP Course

1

23

65

51

140

2

AP Courses

0

4

48

83

135

3 or More AP Courses

0

0

4

54

58







312

323

394

321

1350

a.

b. Give the marginal distribution of class in terms of percents.







Freshmen

Sophs

Juniors




Seniors




23.1%

23.9%

29.2%




23.8%

c. Give the marginal distribution of AP status in terms of percents:






















No AP

1 AP

2 AP




3 AP




75.3%

10.4%

10.0%




4.3%

d. Find the conditional distribution of AP status among seniors in percents.



















No AP

1 AP

2 AP




3 AP




41.4%

15.9%

25.9%




16.8%


e. Find the conditional distribution among classes among students taking no AP Courses.




Freshmen

Sophs

Juniors

Seniors

30.6%

29.1%

27.2%

13.1%




  1. Draw a bar chart expressing the distribution (in percents) of students taking various numbers of AP Courses.



  1. Write a sentence describing the information you get from the bar chart in context.

15. Here are some statistics for students of driving age in Montgomery County based on whether or not their parents work.






Student drives

Student doesn't

Total




to school

drive to school
















Both parents work

3,142

4,230

7,372

One parent works

2,104

1,648

3,752

Neither parent works

425

118

543

Total

5,671

5,996

11,667

a. Fill in the totals in the chart above.


b. Give the marginal distribution of student driving habits in terms of percentages:


Student Drives

Student Doesn’t Drive

48.6%

51.4%

c. Give the marginal distribution of parents working status in terms of percentages:




Both Parents Work

One Parent Works

Neither Parent Works

62.6%

31.9%

4.6%

d. Give the conditional distribution of driving habits among students whose both parents work in percents.




Student Drives

Student Doesn’t Drive

42.6%

57.4%

e. Give the conditional distribution of parent work status among students who drive to school.




Both Parents Work

One Parent Works

Neither Parent Works

55.4%

37.1%

7.5%


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