Question

Determine the critical values that would be used in testing each of the following null hypotheses using the classical approach. (Give your answers correct to three decimal places.)

(a) H_o: ρ = 0 vs. H_a: ρ ≠ 0, with n = 18 and α = 0.05
(smaller value)
(larger value)

(b) H_o: ρ = 0 vs. H_a: ρ > 0, with n = 32 and α = 0.01


(c) H_o: ρ = 0 vs. H_a: ρ < 0, with n = 16 and α = 0.05

Answer 1

a)

Given

Hypotheses:

Ho: ρ = 0 vs. Ha: ρ ≠ 0

n = 18

α = 0.05

Degrees of freedom = n -2 = 18 - 2 = 16

This is the case for two tails test.

From the t-table the critical value is

Larger value =

Smaller value =

b)

Given

Ho: ρ = 0 vs. Ha: ρ > 0, with n = 32 and α = 0.01

This is the case for one tails test.

Degrees of freedom = 32 - 2 = 30

From the t-table the critical value is

c)

Given

Ho: ρ = 0 vs. Ha: ρ < 0, with n = 16 and α = 0.05

This is the case for one tails test.

Degrees of freedom = 16-2 = 14

From the t-table the critical value is