Understanding Statistics in the Behavioral Sciences by Robert R. Pagano (z-lib.org).pdf

Questions 12,

A statistics professor conducts a study to investigate the relationship between the performance of his students on exams and their anxiety. Ten students from his class are selected for the experiment. Just before

taking the final exam, the 10 students are given a n

anxiety questionnaire. Here are final exam and anxiety scores for the 10 students:

Student No. 1 2 3 4 5 6 7 8 9 10

Anxiety 28 41 35 39 31 42 50 46 45 37

Final Exam 82 58 63 89 92 64 55 70 51 72

a. On a piece of graph paper, construct a scatter plot

of the paired scores. Use anxiety as the X variable.

b. Describe the relationship shown in the graph.

c. Assuming the relationship is linear, compute the

value of Pearson r.

d. Determine the least-squares regression line f or

predicting the final exam score, given the anxiety

level. Should bY

be positive or negative? Why?

e. Draw the least-squares regression line of part d on

the scatter plot of part a.

f. Based on the data of the 10 students, if a student

has an anxiety score of 38, what value would you

predict for her final exam score? (Round to two

decimal places.)

g. Calculate the standard error of estimate for predicting final exam scores from anxiety scores .

16,

In Chapter 6, Problem 16 (p. 151), data were presented

on the relationship between birth weight and the sub[1]sequent I Q of seven randomly selected psychology

majors from a particular university. The data are again

presented below.

Student

Birth Weight

(lbs) IQ

1 5.8 122

2 6.5 120

3 8.0 129

4 5.9 112

5 8.5 127

6 7.2 116

7 9.0 130

a. Assuming there is a linear relationship, use these

data and det ermine the least-squares regression

line for predicting IQ, given birth weight.

b. Using this regression line, what IQ would you predict for a birth weigh

19

In Chapter 6, Problem 24 (p. 154), data were shown

on the relationship between the work performance of

10 workers r andomly chosen f rom t he m anufactur[1]ing se ction of a la rge cor poration a nd t wo possible

screening tests. The data are again shown below.

In t hat pro blem y ou w ere a sked to re commend

which of the two tests should be used as a sc reening

device for prospective employees for that section of the

company. On the basis of the data presented, you rec[1]ommended using test 2. Now the question is: Would it

be better to use both test 1 and test 2, rather than test

2 alone? Explain your answer, using R

2

and r

2

. Use a

computer and statistical software to solve this problem

if you have access to them. I/O

Employee

1 2 3 4 5 6 7 8 910

Work performance 50 74 62 90 98 52 68 80 88 76

Test 1 10 19 20 20 21 14 10 24 16 14

Test 2 25 35 40 49 50 29 32 44 46 35

1. Use the data from assignment 6 (Financial Stability and Life Satis

person	Financial Stability	Life Satisfaction	Stability2	Satisfaction2	Stability * Satisfaction
1	75	42	5625	1764	3150
2	50	45	2500	2025	2250
3	27	23	729	529	621
4	60	34	3600	1156	2040
5	5	33	25	1089	165
6	22	16	484	256	352
7	6	11	36	121	66
8	71	38	5041	1444	2698
9	2	23	4	529	46
10	9	18	81	324	162
11	32	44	1024	1936	1408
12	40	21	1600	441	840
SUM	399	348	20749	11614	13798
St Dev	26.08073	11.762807	2017.3864	691.947822	1120.793293

a) What is the regression line predicting Life Satisfaction scores from Financial Stability?

person	Financial Stability	Life Satisfaction	Stability2	Satisfaction2	Stability * Satisfaction
1	75	42	5625	1764	3150
2	50	45	2500	2025	2250
3	27	23	729	529	621
4	60	34	3600	1156	2040
5	5	33	25	1089	165
6	22	16	484	256	352
7	6	11	36	121	66
8	71	38	5041	1444	2698
9	2	23	4	529	46
10	9	18	81	324	162
11	32	44	1024	1936	1408
12	40	21	1600	441	840
SUM	399	348	20749	11614	13798
St Dev	26.08073	11.762807	2017.3864	691.947822	1120.793293

b) Draw the scatterplot and the regression line

c) If someone had a Financial Stability score of 48 what would you predict their Life Satisfaction Scores score to be?

d) What is the standard Error of the Estimate?

2. There has been some research showing that a person's income is related to their intelligence as well as their parent's income. You measure the incomes, intelligence and parental income of multiple people and get the following correlations.

Parent's Income Intelligence

Income .64 .39

Intelligence .53 1

a) How much variance in Income can be accounted for by Intelligence and Parent's Income?

b) What is the multiple correlation coefficient (i.e., R)?

c) If you know the parent's income, how important is it to know a person's intelligence when predicting their income? statistical evidence for answer.

3. Determine the regression equation using the following information.

r = -.85 N=25 S²x=134.24 S²y=381.25 X=434 Y=820