Question

A school counselor noticed that students seemed to have a more depressed mood as finals approach. Based on this observation she wondered if there might a relationship between the students’ workload in a given month and their level of depressed mood. Specifically, she recorded the number of tests and quizzes eight students had in a given month and also assessed their levels of depressed mood at the end of the month. Higher numbers indicate more depressed mood. She decides to conduct a two-tailed test. Calculate Pearson's r.

Participant Number of Tests and Quizzes (X) Depressed Mood (Y) A 12 9 B 3 2 C 12 7 D 2 8 E 2 6 F 6 8 G 5 5 H 4 3 I 8 7 M = 6.0000 SD = 3.90512 M = 6.1111 SD = 2.36878

		.64
		.78
		.16
		.50
		.04

Answer 1

Given that

X=Number of Tests and Quizzes

Y=Depressed Mood

We know the following

n=9 is the sample size

We get the following

The covariance of XY is

The correlation coefficient is

ans: Pearson's r is 0.50

she wondered if there might a relationship between the students’ workload in a given month and their level of depressed mood. Let be the true value of the correlation coefficient. There might a relationship between the 2 variable if is not equal to 0

The hypotheses are

The test statistic is

The degrees of freedom are n-2=9-2=7

This is a 2 tailed test (the alternative hypothesis has "not equal to"). Assuming a 5% level of significance () , the right tail critical value is

Using the t table for df=7 and the area under the right tail=0.025, we get

The critical values are -2.365,+2.365

We will reject the null hypothesis, if the test statistic lies outside the interval ( -2.365,+2.365).

Here, the test statistic is 1.5275 and it lies within the interval ( -2.365,+2.365). Hence we do not reject the null hypothesis.

ans: Fail to reject H₀. There is no significant linear relationship between the students’ workload in a given month and their level of depressed mood