Question

16. The correlation coefficient ρ between two variables is-0.38 for a sample of 35 observations. The null hypothesis is H0 : ρ =0. Which of the following is a correct conclusion based on the data given? Use the 0.02 significance level.

A. Reject the null H0. There is a negative association between the variables.

B. Do not reject the null H0. There is no association between the variables.

C. Reject the null H0. There is a positive association between the variables.

D. Thereisinsufficientinformationtodrawaconclusion.

Answer 1

The test statistic formula is given as below:

t = r*sqrt(n – 2)/sqrt(1 – r^2)

t = (-0.38)*sqrt(35 - 2)/sqrt(1 - (-0.38)^2)

t = -2.35996

Test statistic = -2.35996

df = n - 2 = 35 – 2 = 33

P-value = 0.024343

(by using t-table)

P-value > α = 0.02

So, we do not reject the null hypothesis.

Answer:

B. Do not reject the null H0. There is no association between the variables.