Question

Use the sample correlation r=0.42 and the sample size n=25 to see if there is evidence that the population correlation between the two variables is different than zero.

(a) What are the null and alternative hypotheses?

(b) What is the test statistic?
Round your answer to three decimal places

(c) What are the degrees of freedom?
Enter the exact answer.

(d) What is the p-value.
Round your answer to three decimal places.

(e) What is the conclusion, using a 5% significance level?

(f) Is there evidence that the correlation is different than zero?

Answer 1

(a) Here

Null Hypothesis : H₀ : r = 0

Alternative Hypothsis : H_a : r $\neq$ 0

here test statisitc

t = r sqrt [(n - 2)/ (1 -r²)]

t = 0.42 * sqrt [(25 - 2)/(1- 0.42²)]

t = 0.42 * sqrt [23/0.8236]

t = 2.2195

(c) Here degree of freedom dF = 25 - 2 = 23

(d) p - value = 2 * Pr(t > 2.2195; 23) = 2 * 0.0183 = 0.0366

(e) Here we conclude that at 5% significance level, p - value is less than the significance value so here we reject the null hypothesis.

(f) Here there is evidence that the correlation is different than zero.