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

Answer:

a)

To determine the critical value

Here we need to take the two tailed test as it deals with equal and non equal cases.

n = 18

alpha = 0.05

degree of freedom = n -1

= 18 -1

= 17

critical value t(0.025,17) = 2.110

b)

Given,

n = 32

alpha = 0.01

degree of freedom = 32 - 1

= 31

We need to take the one tailed test,as we are only concerned about the greater than cases

Critical value t(0.01,31)=2.744

c)

n = 16

alpha = 0.05

degree of freedom = 16 - 1

= 15

We need to take the one tailed test,as we are only concerned about the less than cases

critical value t(0.05,15)=1.753