Question

1. A researcher was interested in whether there was a relationship between stress and depression scores obtained from emergency health care providers. The data from 10 emergency workers are below.

Stress	Depression
38	26
28	16
42	34
18	22
26	15
45	24
32	18
26	18
22	12
33	15

Stress M = 31 , SD = 8.25

Depression M = 20, SD = 6.24

1. By hand, calculate the correlation coefficient. You are given the mean and standard deviation already, so you do not need to do that step.

2. Test the statistical significance of the correlation coefficient using the five steps of hypothesis testing.

Step 1: Restate the question as a research hypothesis and a null hypothesis about the populations.

Step 2: Determine the characteristics of the comparison distribution.

Step 3: Determine the cutoff sample score on the comparison distribution at which the null hypothesis should be rejected.

Step 4. Determine your sample’s score on the comparison distribution.

Remember:

Step 5. Decide whether to reject the null hypothesis.

c) Using SPSS, calculate the correlation coefficient and statistical significance. Paste the correlation table from SPSS below.

Answer 1

Answer of a:

Stress	Depression	(x-xbar)	(y-Ybar)	(X-xbar)*(y-ybar)	(x-xbar)2	(y-Ybar)2
38	26	7	6	42	49	36
28	16	-3	-4	12	9	16
42	34	11	14	154	121	196
18	22	-13	2	-26	169	4
26	15	-5	-5	25	25	25
45	24	14	4	56	196	16
32	18	1	-2	-2	1	4
26	18	-5	-2	10	25	4
22	12	-9	-8	72	81	64
33	15	2	-5	-10	4	25
				333	680	390

Correlation Coefficient

Correlation Coefficient = 0.6466

Answer of b:

Step-1

Null hypothesis: There was no significant relationship between stress and depression scores obtained from emergency health care providers

Research Hypothesis: There was a significant relationship between stress and depression scores obtained from emergency health care providers

Step-2

Step-3

t = 1.8289/0.7628

t= 2.3979

Step-4

t-table value = t (0.05, 8) = 2.3060

Step-5

Here, t-calculated is > t-table value, hence we reject null hypothesis. Which means that there was significant relationship between stress and depression scores obtained from emergency health care providers.

Answer of C:

Correlations
		Stress	Depression
Stress	Pearson Correlation	1	.647*
Sig. (2-tailed)		0.043
N	10	10
Depression	Pearson Correlation	.647*	1
Sig. (2-tailed)	0.043
N	10	10
*. Correlation is significant at the 0.05 level (2-tailed).