Question

ch 23 we want to test whether proportions from two populations are different from each other. what are the appropriate null and alternative hypotheses?
○ h0: p1 ≠ p2, ha: p1 = p2
● h0: p̂1 = p̂2, ha: p̂1 ≠ p̂2
○ h0: p1 = p2, ha: p1 > p2
○ h0: p1 = p2, ha: p1 ≠ p2

question 19
1 pts
ch 23* in 2012, respondents to the general social survey were asked: \there are always some people whose ideas are considered bad or dangerous by other people. for instance, somebody who is against churches and religion. if such a person wanted to make a speech in your (city/town/community) against churches and religion, should he be allowed to speak, or not?\
among the 573 male respondents, 459 said, \allow,\ whereas among the 719 female respondents, 552 said, \allow.\ is there a difference between the proportion of males and the proportion of females who would allow an anti - religionist to speak?
take p_m and p_f to be the proportions of all males and females who would allow an anti - religionist to speak. the z test for comparing the proportions of males and females who would allow an anti - religionist to speak has

Explanation:

Step1: Understand Hypothesis Testing Basics

In hypothesis testing for comparing two population proportions \(p_1\) and \(p_2\), the null hypothesis \(H_0\) assumes no difference between the population proportions. The alternative hypothesis \(H_a\) is what we are trying to find evidence for. If we want to test if the proportions are different, the null hypothesis is \(H_0:p_1 = p_2\) (where \(p_1\) and \(p_2\) are the population - level proportions) and the alternative hypothesis is \(H_a:p_1
eq p_2\).

Step2: Analyze Each Option

• Option 1: \(H_0:p1

eq p2, Ha:p1 = p2\) is incorrect. The null hypothesis should assume no difference (equality) when we start the test.

• Option 2: \(H_0:\hat{p}1=\hat{p}2, Ha:\hat{p}1

eq\hat{p}2\) is incorrect. \(\hat{p}\) represents sample proportions. Hypotheses are about population proportions \(p\).

• Option 3: \(H0:p1 = p2, Ha:p1>p2\) is incorrect. This is a one - sided (right - tailed) alternative, but we want to test for a difference (two - sided).
• Option 4: \(H0:p1 = p2, Ha:p1

eq p2\) is correct as it follows the rules of hypothesis testing for a two - sided test of two population proportions.

Answer:

D. \(H0:p1 = p2, Ha:p1
eq p2\)