Question

6. To determine the relationship between two variables while holding a third one constant you should calculate a ___________

A. Point biserial correlation

B. Partial correlation

C. Pearson correlation

D. Spearman correlation.

7. A candy bar manufacturer is interested in trying to estimate how sales are influenced by the price of their product. To do this, the company randomly chooses 6 small cities and offers the candy bar at different prices. What is the correlation between candy price and sales?

City Price ($) Sales

Miami 1.30 100

McKinney 1.60 90

Newberg   1.80 90

Prescott 2.00 40

Tacoma 2.40    38

San Jose 2.90 32

8. A teacher records the scores on a midterm quiz and on the final exam for 8 of her students. She finds that there is a correlation of .896 between the two scores. Calculate the coefficient of determination.

9. A previous statistics class kept records of the number of hours they studied and their score on the final 20 point quiz. Here are the data collected

. hours studied quiz score

X Y

8 18

6 14

5 13

7 15

4 10

Conduct a hypothesis test to investigate whether there is a significant relationship between X and Y, using α= .10

10. In a study of diagnostic processes, entering clinical graduate students are shown a 20-minute videotape of children’s behavior and asked to rank-order 10 behavioral events on the tape in the order of the importance, 1 = most important, and 10 = least important. The data are then averaged to produce an average rank ordering for the entire class. The same thing was then done using experienced clinicians. The data follow: Events Clinicians Student 1 1 2

2 3 4

3 2 1

4 7 6

5 5 5

6 4 3

7 8 10

8 6 8

9 9 7

10 10 9

Use Spearman’s r, to measure the agreement between experienced and novice clinicians.

Answer 1

Q.6 ans :- B.Partial correlation coefficient.

Q.7 X-prices

       Y-sales

        Correlation between prices and sales

city	X	Y
1	1.3	100
2	1.6	90
3	1.8	90
4	2	40
5	2.4	38
6	2.9	32

      

By using MS-Excel, correlation coefficient=r=CORREL (G5:G10,H5:H10)= -0.8854

As prices increases sales decreases for the given data.

Q.8 r=0.896

        Coefficient of determination=r2=0.802816.

Q.9 X=no.of hours of study

       Y=scores

        r = 0.976187

To test whether there is a significant relationship between X&Y at α=0.10

               H0 : ƿ=0

               H1: ƿ≠0

t = ~t(n-2) d.f

tcal=7.794229, t(n-2) d.f=2.3533

tcal> t(n-2) d.f ,   we reject H0 and conclude that X & Y are correlated.

Q.10

events	Clinicians	student	di	di^2
1	1	2	-1	1
2	3	4	-1	1
3	2	1	1	1
4	7	6	1	1
5	5	5	0	0
6	4	3	1	1
7	8	10	-2	4
8	6	8	-2	4
9	9	7	2	4
10	10	9	1	1
Total				18

Spearmans rank correlation coefficient : 1 - =0.890909

                                       Here di = rank (xi)-rank(yi).