Question

Two separate tests are designed to measure a student's ability to solve problems. Several students are randomly selected to take both test and the results are give below Test A | 64 48 51 59 60 43 41 42 35 50 45 Test B | 91 68 80 92 91 67 65 67 56 78 71 (a) What is the value of the linear coefficient r (b) Assuming a 0.05 level of significance, what is the critical value

Answer 1

The linear coefficient r can be calculated using the sum of the squares of residuals and the total sum of squares SST.

Step-by-step explanation:

(a) The value of the linear coefficient r can be calculated using the formula:

r = sqrt((SSR / SST)), where SSR is the sum of the squares of the residuals and SST is the total sum of squares.

(b) The critical value can be obtained from a Table of Critical Values for the sample correlation coefficient using the degrees of freedom (df = n - 2), where n is the number of data points.

Answer 2

a) r = 0.974

b) Critical value = 0.602

Step-by-step explanation:

Given - Two separate tests are designed to measure a student's ability to solve problems. Several students are randomly selected to take both test and the results are give below

Test A | 64 48 51 59 60 43 41 42 35 50 45

Test B | 91 68 80 92 91 67 65 67 56 78 71

To find - (a) What is the value of the linear coefficient r ?

(b) Assuming a 0.05 level of significance, what is the critical value ?

Proof -

A)

r = 0.974

B)

Critical Values for the Correlation Coefficient

n alpha = .05 alpha = .01

4 0.95 0.99

5 0.878 0.959

6 0.811 0.917

7 0.754 0.875

8 0.707 0.834

9 0.666 0.798

10 0.632 0.765

11 0.602 0.735

12 0.576 0.708

13 0.553 0.684

14 0.532 0.661

So,

Critical r = 0.602 for n = 11 and alpha = 0.05