Question

A test of H₀: p = 0.5 versus H_a: p > 0.5 has the test statistic z = 1.15.

Part A: What conclusion can you draw at the 5% significance level? At the 1% significance level? (6 points)

Part B: If the alternative hypothesis is H_a: p ≠ 0.5, what conclusion can you draw at the 5% significance level? At the 1% significance level?

Answer 1

Solution:

z = 1.15

Part A:

This is a right tailed test.

P-value = P(Z > 1.15 )

= 1 - P(Z < 1.15 )

= 1 - 0.8749

= 0.1251

Therefore, P-value = 0.1251 > 0.05, it is concluded that fail to reject null hypothesis.

P-value = 0.1251 > 0.01, it is concluded that fail to reject null hypothesis.

Part B :

This is a two tailed hypothesis,

P-value =2* P(Z > 1.15 )

= 2 * (1 - P(Z < 1.15 ))

= 2 * (1 - 0.8749)

= 0.2502

Therefore, P-value = 0.2502 > 0.05, it is concluded that fail to reject null hypothesis.

P-value = 0.2502 > 0.01, it is concluded that fail to reject null hypothesis.