Question

Test H0: π = 0.25 versus HA: π  0.25 with p = 0.34 and n = 100 at alpha = 0.05 and 0.01.

Answer 1

Given that, n = 100 and p = 0.34

The null and alternative hypotheses are,

H0 : π = 0.25

HA : π ≠ 0.25

This hypothesis test is a two-tailed test.

Test statistic is,

=> Test statistic = 2.08

p-value = 2 * P(Z > 2.08)

=> p-value = 2 * [ 1 - P(Z < 2.08) ]

=> p-value = 2 * [ 1 - 0.9812 ]

=> p-value = 2 * 0.0188

=> p-value = 0.0376

Since, p-value is less than alpha = 0.05, we reject H0.

​​​​​​Since, p-value is greater than alpha = 0.01, we fail to reject H0.

Therefore, we Reject H0 at alpha = 0.05 but do not reject H0 at alpha = 0.01