Chapter 9, Problem 1CQQ

In Exercises 1-4, use the following surrey results: Randomly selected subjects were asked if they agreed with the statement “It is morally wrong for married people to hate an affair.” Among the 386 women surveyed, 347 agreed with the statement. Among the 359 men surveyed, 305 agreed with the statement (based on data from a Pew Research poll).

1. Identify the null and alternative hypotheses resulting from the claim that the proportion of women who agree with the given statement is equal to the proportion of men who agree.

To determine

To identify: The null and alternative hypotheses.

Answer to Problem 1CQQ

Null hypothesis: $H_0:p_1=p_2$

Alternative hypothesis: $H_1:p_1\ne p_2$

Explanation of Solution

Given info:

The claim for the hypothesis test is that the proportion of women who agree with the given statement is equal to the proportion of men who agree.

Justification:

Let population 1 denotes the women and population 2 denotes the men.

Let $p_1$ be the proportion of women and $p_2$ be the proportion of men.

Here, the given claim is the proportion of women who agree with the given statement is equal to the proportion of men who agree. This indicates that $p_1$ equal to $p_2$.

Null hypothesis:

$H_0:p_1=p_2$

That is, the proportion of women who agree with the given statement is equal to the proportion of men who agree.

Alternative hypothesis:

$H_1:p_1\ne p_2$

That is, the proportion of women who agree with the given statement is not equal to the proportion of men who agree.