Question

The researchers report that the results were statistically significant at the $1\%$level. Which of the following is the most appropriate conclusion?

a. Because the $P$-value is less than $1\%$, fail to reject $H_0$. There is not

convincing evidence that the proportion of male college students in the study who

worked for pay last summer is different from the proportion of female college students in the study who worked for pay last summer.

b. Because the $P$-value is less than $1\%$, fail to reject $H_0$. There is not

convincing evidence that the proportion of all male college students who worked for pay last summer is different from the proportion of all female college students who worked for pay last summer.

c. Because the $P$-value is less than $1\%$, reject $H_0$. There is convincing

evidence that the proportion of all male college students who worked for pay last

summer is the same as the proportion of all female college students who worked for pay last summer.

d. Because the $P$-value is less than $1\%$, reject $H_0$. There is convincing

evidence that the proportion of all male college students in the study who worked for pay last summer is different from the proportion of all female college students in the study who worked for pay last summer.

e. Because the $P$-value is less than $1\%$, reject $H_0$ . There is convincing

evidence that the proportion of all male college students who worked for pay last

summer is different from the proportion of all female college students who worked for pay last summer.

Short answer

Option (e) is correct.

Step-by-step solution

Given Information

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.

Claim: Difference in proportion of males and females.

Explanation

As $p_M\ne p_F$

The appropriate hypothesis as per given conditions is:

Null: $H_0:p_M=p_F$

Alternative Hypothesis: $H_a:p_M\ne p_F$

Now, the results are significant at the $1\%$significance level which implies that we rejected the null hypothesis. In case we reject the null hypothesis if the $P$value is less than the significance level and hence the $\mathrm{P}$value is then less than $1\%$in this case.

As we rejected the null hypothesis, there is evidence that population proportion are different.

Option (e) is correct.