Chapter 10.1, Problem 32E

To determine

To select from the option that which of the following is the most appropriate conclusion.

Answer to Problem 32E

The option (e) 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:

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

We have given also that the results are significant at the $1\%$ significance level which implies that we rejected the null hypothesis. Now, if we reject the null hypothesis if the P value is less than the significance level and thus the P value is then less than $1\%$ in this case.

Since we rejected the null hypothesis there is a significant evidence that the proportions in the populations are different and thus the option (e) is the correct option.