Question

Determine the critical value or values for a one-mean z-test at the 10% significance level if the hypothesis test is left-tailed (Ha:μ<μ0).

z0.10 1.282

z0.05 1.645

z0.025 1.960

z0.01 2.326

z0.005 2.576

Answer 1

Solution :

Given that,

This is the left tailed test,

= 0.10

P(Z > z) = 0.10

1 - P(Z < z) = 0.10

P(Z < z) = 1 - 0.10

P(Z < 1.228) = 0.9

z = 1.228

critical value = 1.228

= 0.05

P(Z > z) = 0.05

1 - P(Z < z) = 0.05

P(Z < z) = 1 - 0.05

P(Z < 1.645) = 0.95

z = 1.645

critical value = 1.645

= 0.025

P(Z > z) = 0.025

1 - P(Z < z) = 0.025

P(Z < z) = 1 - 0.025

P(Z < 1.960) = 0.975

z = 1.960

critical value = 1.960

= 0.01

P(Z > z) =0.01

1 - P(Z < z) = 0.01

P(Z < z) = 1 - 0.01

P(Z < 2.326) = 0.0.99

z = 2.326

critical value = 2.326

= 0.005

P(Z > z) = 0.005

1 - P(Z < z) = 0.005

P(Z < z) = 1 - 0.005

P(Z < 2.576) = 0.995

z = 2.576

critical value = 2.576