Time to Practice – Week Five

Complete Parts A, B, and C below.

Part A

Some questions in Part A require that you access data from Statistics for People Who (Think They) Hate Statistics. This data is available on the student website under the Student Text Resources link.

1.     Use the following data to answer Questions 1a and 1b.

Total no. of problems correct (out of a possible 20)

Attitude toward test taking (out of a possible 100)

17

94

13

73

12

59

15

80

16

93

14

85

16

66

16

79

18

77

19

91

a.     Compute the Pearson product-moment correlation coefficient by hand and show all your work.

b.     Construct a scatterplot for these 10 values by hand. Based on the scatterplot, would you predict the correlation to be direct or indirect? Why?

2.     Rank the following correlation coefficients on strength of their relationship (list the weakest first):

+.71

+.36

–.45

.47

–.62

3.     Use IBM® SPSS® software to determine the correlation between hours of studying and grade point average for these honor students. Why is the correlation so low?

Hours of studying

GPA

23

3.95

12

3.90

15

4.00

14

3.76

16

3.97

21

3.89

14

3.66

11

3.91

18

3.80

9

3.89

4.     Look at the following table. What type of correlation coefficient would you use to examine the relationship between sex (defined as male or female) and political affiliation?

How about family configuration (two-parent or single-parent) and high school GPA? Explain why you selected the answers you did.

Level of Measurement and Examples

Variable X

Variable Y

Type of correlation

Correlation being computed

Nominal (voting preference, such as Republican or Democrat)

Nominal (gender, such as male or female)

Phi coefficient

The correlation between voting preference and gender

Nominal (social class, such as high, medium, or low)

Ordinal (rank in high school graduating class)

Rank biserial coefficient

The correlation between social class and rank in high school

Nominal (family configuration, such as intact or single parent)

Point biserial

The correlation between family configuration and grade point average

Ordinal (height converted to rank)

Ordinal (weight converted to rank)

Spearman rank correlation coefficient

The correlation between height and weight

Interval (number of problems solved)

Interval (age in years)

Pearson product-moment correlation coefficient

The correlation between number of problems solved and the age in years

5.     When two variables are correlated (such as strength and running speed), it also means that they are associated with one another. But if they are associated with one another, then why does one not cause the other?

6.     Given the following information, use Table B.4 in Appendix B of Statistics for People Who (Think They) Hate Statistics to determine whether the correlations are significant and how you would interpret the results.

a.     The correlation between speed and strength for 20 women is .567. Test these results at the .01 level using a one-tailed test.

b.     The correlation between the number correct on a math test and the time it takes to complete the test is –.45. Test whether this correlation is significant for 80 children at the .05 level of significance. Choose either a one- or a two-tailed test and justify your choice.

c.     The correlation between number of friends and grade point average (GPA) for 50 adolescents is .37. Is this significant at the .05 level for a two-tailed test?

7.     Use the data in Ch. 15 Data Set 3 to answer the questions below. Do this one manually or use IBM® SPSS® software.

a.     Compute the correlation between income and level of education.

b.     Test for the significance of the correlation.

c.     What argument can you make to support the conclusion that lower levels of education cause low income?

8.     Use the following data set to answer the questions. Do this one manually.

a.     Compute the correlation between age in months and number of words known.

b.     Test for the significance of the correlation at the .05 level of significance.

c.     Recall what you learned in Ch. 5 of Salkind (2014)about correlation coefficients and interpret this correlation.

Age in months

Number of words known

12

6

15

8

9

4

7

5

18

14

24

18

15

7

16

6

21

12

15

17

9.     How does linear regression differ from analysis of variance?

10.  Betsy is interested in predicting how many 75-year-olds will develop Alzheimer’s disease and is using level of education and general physical health graded on a scale from 1 to 10 as predictors. But she is interested in using other predictor variables as well. Answer the following questions.

a.     What criteria should she use in the selection of other predictors? Why?

b.     Name two other predictors that you think might be related to the development of Alzheimer’s disease.

c.     With the four predictor variables (level of education, general physical health, and the two new ones that you name), draw out what the model of the regression equation would look like.

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