Chapter 10.1, Problem 31E

To determine

To select the best answer from the option for the hypothesis to be tested of all college male sand females who worked last summer.

Answer to Problem 31E

The option (a) is the correct option.

Explanation of Solution

It is given that:

  $p_M$ is the proportion of all college males who worked last summer.

  $p_F$ is the proportion of all college females who worked last summer.

The given claim is that the difference in the proportion for males and females.

That is: $p_M\ne p_F$ .

Thus, the claim is either the null hypothesis or the alternative hypothesis. The null hypothesis states that the population proportions are equal. If the null hypothesis is the claim then the alternative hypothesis states the opposite of the null hypothesis.

Therefore, the appropriate hypotheses for this is:

  $\begin{array}{l}{H}_0:p_M=p_F\\ H_a:p_M\ne p_F\end{array}$

Thus, then solve the inequality, which gives:

  $\begin{array}{l}{H}_0:p_M-p_F=0\\ H_a:p_M-p_F\ne 0\end{array}$

Thus, option (a) is the correct option.