Question

Identify the critical z values and the rejection region of the following:

a) Right-tailed test with a = 0.05

b) Left-tailed test with a = 0.025

c) Two-tailed test with a = 0.01

d) a = 0.10 with H_A : p < 0.26

Answer 1

Identify the critical z values and the rejection region of the following:

a) Right-tailed test with a = 0.05

Critical Z value = 1.6449

Rejection region: Reject H₀ if Z > 1.6449

(By using Z-table or excel)

b) Left-tailed test with a = 0.025

Critical Z value = -1.96

Rejection region: Reject H₀ if Z < -1.96

(By using Z-table or excel)

c) Two-tailed test with a = 0.01

Critical Z value = -2.5758 and 2.5758

Rejection region: Reject H₀ if Z < -2.5758 or Z > 2.5758

(By using Z-table or excel)

d) a = 0.10 with HA : p < 0.26

Critical Z value = -1.2816

Rejection region: Reject H₀ if Z < -1.2816

(By using Z-table or excel)

[Hint for Excel: For left tailed test, use =normsinv(?). For right tailed test, use normsinv(1 – ?). For two tailed test, divide significance level ? by 2 and then find critical Z value by using excel command =normsinv(?/2) and =normsinv(1 - ?/2) .]