# Given the following information, use table b.4 (which is right above)

Given the following information, use Table B.4 (which is right above) to determine whether the

1 .9877 .9995 1 .9969 .9999

2 .9000 .9800 2 .9500 .9900

3 .8054 .9343 3 .8783 .9587

4 .7293 .8822 4 .8114 .9172

5 .6694 .832 5 .7545 .8745

6 .6215 .7887 6 .7067 .8343

7 .5822 .7498 7 .6664 .7977

8 .5494 .7155 8 .6319 .7646

9 .5214 .6851 9 .6021 .7348

10 .4973 .6581 10 .5760 .7079

11 .4762 .6339 11 .5529 .6835

12 .4575 .6120 12 .5324 .6614

13 .4409 .5923 13 .5139 .6411

14 .4259 .5742 14 .4973 .6226

15 .412 .5577 15 .4821 .6055

16 .4000 .5425 16 .4683 .5897

17 .3887 .5285 17 .4555 .5751

18 .3783 .5155 18 .4438 .5614

19 .3687 .5034 19 .4329 .5487

20 .3598 .4921 20 .4227 .5368

25 .3233 .4451 25 .3809 .4869

30 .2960 .4093 30 .3494 .4487

35 .2746 .3810 35 .3246 .4182

40 .2573 .3578 40 .3044 .3932

45 .2428 .3384 45 .2875 .3721

50 .2306 .3218 50 .2732 .3541

60 .2108 .2948 60 .2500 .3248

70 .1954 .2737 70 .2319 .3017

80 .1829 .2565 80 .2172 .2830

90 .1726 .2422 90 .2050 .2673

100 .1638 .2301 100 .1946 .2540

1. Given the following information, use Table B.4 (which is right above) to determine whether the correlations are significant and how you would interpret the results.

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

- 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 two-tailed test and justify your choice.
- 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?

2. A study was completed that examined the relationship between coffee consumption and level of stress for a group of 50 undergraduates. The correlation was .373, and it was a two-tailed test, done at the .01 level of significance. First, is the correlation significant? Second, what’s wrong with the following statement? “As a result of the data collected in this study and our rigorous analyses, we have concluded that if you drink less coffee, you will experience less stress.”

3. Use the following set of data to answer the following questions.

- Compute the correlation between age in months and number of words known.
- Test for the significance of the correlation at the .05 level of significance.
- Go way back and recall what you learned in chapter 5 about correlation coefficients and interpret this correlation.

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

- What criteria should she use in the selection of other predictors? Why?
- Name two other predictors that you think might be related to the development of Alzheimer’s disease.
- With the four predictor variables (level of education and general physical health, and the two new ones that you name), draw out what the model of the regression equation would look like. (Do your best to draw on Word or describe it in detail).

5. Peter was curious to know if the average number of games won in a year predicts Super Bowl performance (win or lose). The X variable was the average number of games won during the past 10 seasons. The Y variable was whether the team ever won the Super Bowl during the past 10 seasons. Here are the data:

- How would you assess the usefulness of the average number of wins as a predictor of whether a team ever won a Super Bowl?
- What’s the advantage of being able to use a categorical variable (such as 1 or 0) as a dependent variable?
- What other variables might you use to predict the dependent variable, and why would you choose them?

6. Now for multiple predictor variables. Take a look at the data below with the outcome being a great chef. We suspect that variables such as number of years of experience cooking, level of formal culinary education, and number of different positions (sous chef, pasta station, etc.) all contribute to rankings or scores on the Great Chef Test.

- Which are the best predictors of the Chef’s score?
- What can you expect for a score from a person with 12 years of experience and a Level 2 education, and who has held five positions?