If the decision is to reject the null hypothesis of no difference between two population proportions at the 5% level of significance, what are the alternative hypothesis and rejection region? A) H₀: $\pi$₁ $\neq$ $\pi$₂; z 1.65 and z 1.96 and z $\pi$₂; z $\pi$₂; z

Question

If the decision is to reject the null hypothesis of no difference between two population proportions at the 5% level of significance, what are the alternative hypothesis and rejection region? A) H₀: $\pi$₁ $\neq$ $\pi$₂; z > 1.65 and z < -1.65 B) H₀: $\pi$₁ $\neq$$\pi$₂; z > 1.96 and z < -1.96 C) H₀: $\pi$₁ > $\pi$₂; z < - 1.65 D) H₀: $\pi$₁ > $\pi$₂; z < -1.96F

Quizplus · Accepted Answer

The alternative hypothesis would be that there is a difference between two population proportions (F1F1F1S1F1F1F10), and the rejection region would be z > 1.96 and z < -1.96 since the level of significance is 5%. Option B matches this description. Option A and D have incorrect rejection regions (z > 1.65 and z < -1.65 are for a significance level of 10%), and option C has an incorrect alternative hypothesis (F1F1F1S1F1F1F10₁ > F1F1F1S1F1F1F10₂ is not the alternative hypothesis for a two-sided test).

If the Decision Is to Reject the Null Hypothesis of No