Question

A sample survey interviews SRSs of 500 female college students and 550 male college students. Researchers want to determine whether there is a difference in the proportion of male and female college students who worked for pay last summer. In all, 410 of the females and 484 of the males say they worked for pay last summer. 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
H0.
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
H0.
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
H0.
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
H0.
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
H0.
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.

Answer 1

Answer:

Option (d) and (e)

Step-by-step explanation:

We are given that a sample survey interviews SRS of 500 female college students and 550 male college students. And Researchers want to determine whether there is a difference in the proportion of male and female college students who worked for pay last summer.

In all, 410 of the females and 484 of the males say they worked for pay last summer.

From this, Null Hypothesis, $H_0$ : $p_1 = p_2$ {means proportion of male and female college students who worked for pay last summer are same}

Alternate Hypothesis, $H_1$ : $p_1\neq p_2$ {means there is a difference in the proportion of male and female college students who worked for pay last summer}

Now, since we know that results were statistically significant at the 1% level.

So, if p-value is less than the significance level ⇒ we will reject $H_0$

     if p-value is more than the significance level ⇒ we will not reject $H_0$

From the options given it is sure that P-value is less than 1%,i.e.;

P-value is less than the significance level, so we will reject null hypothesis and conclude that 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.

Also, option (d) and (e) are same in my opinion.