Question

A high school psychologist was concerned about the equivalency of two types of standardized tests given to students as part of their college entrance exams. She set out to see if there was a positive correlation between the two exams. She sampled 5 students who took both exams. Use the data below to answer questions 10-14:

Subject                Test A                   Test B

1                          700                         35

2                          772                         38

3                          605                         36

4                          721                         39

5                          695                         34

10. What is the correlation coefficient?
11. How many tails does the test have?
12. What are the degrees of freedom?
13. What is the critical r value for a level of significance of 0.01?
14. What do you conclude about the data?

Answer 1

Solution :

The null and alternative hypotheses would be as follows :

a) The correlation coefficient is given as follows :

From the above table we get,

The correlation coefficient is 0.4376.

b) The test has one-tail. The test is right-tailed test.

c) Degrees of freedom = (n - 2) = (5 - 2) = 3

d) Significance level = 0.01

The right-tailed critical value of r at 0.01 significance level and 3 degrees of freedom is 0.934.

e) Conclusion :

Since, obtained value of correlation coefficient (r) is less than the critical value of r, therefore we shall be fail to reject the null hypothesis at 0.01 significance level.

At 0.01 there is not sufficient evidence to conclude that a positive correlation exist between the two exams.

Please rate the answer. Thank you.