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

Degree of freedom for Pearson correlation hypothesis testing is given df = n-2 (where n is sample size)

(A) Degree of freedom = n-2 = 18-2 = 16

alpha level = 0.05

t critical = T.INV.2T(alpha,df) (this is excel function)

= T.INV.2T(0.05,16)

= -2.120 and 2.120 (two values for two tailed hypothesis)

(B) Degree of freedom = n-2 = 32-2 = 30

alpha level = 0.01

t critical = T.INV(alpha,df) (this is excel function)

= T.INV(0.01,30)

= 2.457 (right tailed hypothesis)

(C) Degree of freedom = n-2 = 16-2 = 14

alpha level = 0.05

t critical = T.INV(alpha,df) (this is excel function)

= T.INV(0.05,14)

= -1.761 (left tailed hypothesis)