Question

A study of college soccer games revealed the correlation between the number of shots attempted and the number of goals scored to be 0.87 for a sample of 11 games.

        a. State the decision rule for 0.01 significance level: H₀: ρ ≤ 0; H₁: ρ > 0 (Round the final answer to 3 decimal places.)

Reject H₀ if t > ?

b. Compute the value of the test statistic. (Round the final answer to 3 decimal places.)

Value of the test statistic ?

c. What is the p-value? (Round the final answer to 4 decimal places.)

p-value is            ?

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :   0

H_a : > 0

r = 0.87

n = 11

degrees of freedom = n - 2 = 11 - 2 = 9

Test statistic = t

=

= 0.87 * (9) / (1 - 0.87²)

= 0.685

The null hypothesis is rejected , based on the sample correlation provided, we have

that r = 0.87 r _c = 0.685 r = 0.87 > r _c = 0.685, from which is concluded that the null hypothesis is rejected.

p-value = 0.2553