Question

Depression	Anxiety
79	80
87	97
95	85
93	85
86	94
96	94
95	94
98	76
84	61
97	97
97	97
97	88
100	97
89	94
94	88
98	97
98	94
94	73
89	94
93	82
83	79
90	97
88	100
84	91
93	94
86	94
84	88
88	94
92	94
95	89
95	79
83	76

• Perform the appropriate test and provide a narrative write up for the Depression and Anxiety analysis.

Answer 1

Perform the appropriate test and provide a narrative write up for the Depression and Anxiety analysis.

Solution:

Here, we have to use t test for the population correlation coefficient. The null and alternative hypotheses for this test are given as below:

Null hypothesis: H₀: There is no any relationship exists between the depression and anxiety.

Alternative hypothesis: H_a: There is a relationship exists between the depression and anxiety.

H₀: ρ = 0 versus H_a: ρ ≠ 0

This is a two tailed test.

We assume level of significance = α = 0.05

The test statistic formula is given as below:

t = r*sqrt(n – 2)/sqrt(1 – r^2)

From given data, we have

r = 0.26861

n = 32

df = n – 2 = 32 – 2 = 30

t = 0.26861*sqrt(32 - 2)/sqrt(1 - 0.26861^2)

t = 0.26861*sqrt(30)/ 0.963249

t = 1.471238/ 0.963249

t = 1.52737

P-value = 0.1371

(by using t-table or excel)

P-value > α = 0.05

So, we do not reject the null hypothesis

There is insufficient evidence to conclude that there is a relationship exists between the depression and anxiety.