UST LEARNING ENHANCER PROBLEM QUESTIONS SOLUTION

UST LEARNING ENHANCER PROBLEM QUESTIONS SOLUTION

Subject: Education    / General Education
Question

We sample 20 new cars (sedans) and find the average miles per gallon (mpg) to be 26 with a standard deviation of 1.7.

1) If we increase our sample size to 40, what is the standard error of the mean?

In a sample of 100 BSC students, we find that on average students eat at a fast-food restaurant four times a week with a standard deviation of .5.

2) What is the standard error of the mean?

3) If our sample size is 1000, what is the standard error?

In a sample of 212 BSC students, we find that 82% are binge drinkers.

4) If we increase the sample size to 500, what is the standard error of the proportion?

Thirty out of 167 students have been involved in a violent conflict in in the past year.

5) If 90 students reported a violent conflict, what is the standard error of the proportions?

We sample 20 news cars (sedans) and find the average mpg to be 26 with a standard deviation of 1.7.

6) What is the 95% confidence interval (CI)

In a sample of 100 BSC students, we find that on average students eat at a fast-food restaurant four times a week with a standard deviation of .5.

7) What is the 95% CI?

8) What is the 99% CI?

In a sample of 212 BSC students, we find that 82% are binge-drinkers

9) What is the 99% CI?

EXERCISE 2

Use the cross-tabulation below to answer questions 1-3.

Homeowner or Renter of Respondent Cross-tabulation

WHITE

BLACK

OTHER

TOTAL

Homeowner or renter Owns home

Pays rent

Other

590

241

23

45

57

4

27

24

3

662

322

28

Total

852

106

54

1012

1) How many respondents own a home?

2) Of Whites, what percent own a home?

3) Which of the three groups is most likely to pay rent?

Use the table below to answer questions 4 & 5

Rap Music (3) Respondent’s Sex Cross-tabulation

MALE

FEMALE

TOTAL

Rap Music (3) Like it

Mixed feelings

Dislike it

Count

% Within

Respondent’s sex

Count

% Within respondent’s sex

Count

% Within respondent’s sex

56

15.3%

60

16.4%

250

68.3%

55

11.1%

109

22.0%

332

66.9%

111

12.9%

169

19.6%

582

67.5%

Total

Count

% Within respondents sex

366

100.0%

496

100.0%

862

100.0%

4) Of females, what percent like a rap music?

5) Are males or females more likely to like rap music?

Suppose that we want to know if males are more likely than females to live off campus. Use the data below to construct a cross-tabulation table. Be sure to include frequencies, column percent’s, and marginal values.

SEX

RESIDENCE

SEX

RESIDENCE

Male

Female

Female

Female

Male

Female

Female

Male

Female

Female

Female

Male

On-Campus

On-Campus

On-Campus

On-Campus

On-Campus

On-Campus

On-Campus

On-Campus

On-Campus

On-Campus

On-Campus

On-Campus

Female

Female

Female

Female

Male

Female

Female

Female

Male

Female

Female

On Campus

On Campus

On Campus

On Campus

On Campus

On Campus

On Campus

On Campus

On Campus

On Campus

On Campus

6) What percent of respondents are male?

7) Of females, what percent live off-campus?

8) Of those who live off-campus, what percent are female?

9) Use the table below to calculate chi-square:

Voting in 1992 election

Frequency

Percent

Valid Percent

Cumulative percent

Valid Voted

Did not vote

Not eligible

Refused

659

211

20

5

73.2

23.4

2.2

.6

73.6

23.6

2.2

.6

73.6

97.2

99.4

100.0

Total

Missing DK

NA

895

3

2

99.4

.3

.2

100.00

Total

Total

5

900

.6

100.0

10) Use the table below to calculate chi square:

Classical music (3) Education cross-tabulation

Less Than High School

High School of higher

Total

Classical music (3) Like it

Mixed Feelings

Dislike it

Count

% Within education

Count

% Within education

Count

% Within education

35

30.4%

23

20.0%

57

49.6%

403

54.2%

196

26.3%

145

19.5%

438

51.0%

219

25.5%

202

23.5%

Total

Count

% Within education

115

100.0%

744

100.0%

859

100.0%

For each of the problems below:

A) Draw a scatterplot.

B) Calculate Pearson’s r

C) Calculate the y-intercept, slope, and draw a regression line on the scatterplot.

D)Answer the “prediction” problem

E) Calculate r2 and explain what it tells us about the relationship between the variables

F) Calculate the t-ratio for Pearson’s r and determine the level of significance

11) A researcher wants to learn more about the relationship between the number of miles traveled to work and earnings. She hypothesizes that wealthier employees live outside the city rather than in the city and decides to sample a group of workers from a bank located downtown. She obtains the following data.

EARNINGS IN $ (X)

MILES TRAVELED TO WORK (Y)

33,250

84,500

66,350

58,425

45,600

67,240

77,900

5

21

6

7

8

14

10

Prediction problem: How far from the city does an employee earning 50,000 live?

12) A researcher wants to investigate the relationship between social networks and virtual social networks. She predicts that large virtual networks will be associated with large “real” networks. She develops two networking indices to measure networking that range from 0 to 50. Use the data below to access her hypothesis.

VIRTUAL SOCIAL NETWORKING SCORE (X)

“REAL SOCIAL NETWORKING SCORE (Y)

25

32

16

10

48

22

15

25

34

41

20

10

23

19

37

25

41

25

26

18

Prediction problem: What is the “real” networking score for a respondent with a virtual networking score of 30?

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