Question

Consider the following competing hypotheses:

H₀: ρ_xy ≥ 0
H_A: ρ_xy < 0

The sample consists of 32 observations and the sample correlation coefficient is –0.35. [You may find it useful to reference the t table.]

a-1. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)

a-2. Find the p-value.

A)0.025

p-value < 0.05

B)0.01    p-value < 0.025

C)p-value < 0.01

D)p-value  0.10

E)0.05  p-value < 0.10

Answer 1

Solution :

This is the left tailed test .

The null and alternative hypothesis is ,

H₀ :   = 0

H_a : < 0

degrees of freedom = n - 2 = 32 - 2 = 30

Test statistic = t

=

= -0.35 * (30) / (1 - (-0.35)²)

= -2.046

P-value = 0.0248

B)0.01    p-value < 0.025