Question

A high school teacher hypothesizes a negative relationship between performance in exams and performance in presentations. To examine this, the teacher computes a correlation of 0.58 from a random sample of 18 students from class. What can the teacher conclude with an α of 0.01?

a) Compute the appropriate test statistic(s) to make a decision about H₀.
(Hint: Make sure to write down the null and alternative hypotheses to help solve the problem.)
critical value =  ; test statistic =
Decision:  ---Select--- Reject H0 Fail to reject H0

b) Compute the corresponding effect size(s) and indicate magnitude(s).
If not appropriate, input and/or select "na" below.
effect size =  ;   ---Select--- na trivial effect small effect medium effect large effect

c) Make an interpretation based on the results.

There is a significant positive relationship between performance in exams and performance in presentations.There is a significant negative relationship between performance in exams and performance in presentations.    There is no significant relationship between performance in exams and performance in presentations.

Answer 1

Let denotes correlation coefficient between performance in exams and performance in presentations.

a) critical value = -2.583 and value of test statistic = 2.848

b) The corresponding effect size = r² = 0.58² = 0.3364, medium effect

c) There is a significant positive relationship between performance in exams and performance in presentations.