A national poll by the Institute for College Access and Success showed that in 69% of college graduates from public and nonprofit colleges in 2013 had student loan debt. Dr. Blackman wanted to find out if her public nonprofit university had a lower proportion of students who graduated with student loan debt in 2013.For this survey, the null hypothesis was that the proportion of students with graduated with student loan debt equals 69% and the alternative hypothesis is that the proportion with student loan debt does not equal 69%. The significance level for this test was 0.05.The results of the hypothesis test of the new survey showed a p-value of 0.039.Which of the following statements is correct? Check all that apply. The results were statistically significant. The results were not statistically significant. The null hypothesis should be rejected. The null hypothesis should be accepted. The null hypothesis cannot be rejected.
Question
A national poll by the Institute for College Access and Success showed that in 69% of college graduates from public and nonprofit colleges in 2013 had student loan debt. Dr. Blackman wanted to find out if her public nonprofit university had a lower proportion of students who graduated with student loan debt in 2013.For this survey, the null hypothesis was that the proportion of students with graduated with student loan debt equals 69% and the alternative hypothesis is that the proportion with student loan debt does not equal 69%. The significance level for this test was 0.05.The results of the hypothesis test of the new survey showed a p-value of 0.039.Which of the following statements is correct? Check all that apply. The results were statistically significant. The results were not statistically significant. The null hypothesis should be rejected. The null hypothesis should be accepted. The null hypothesis cannot be rejected.
Solution
The correct statements are:
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The results were statistically significant. This is because the p-value of 0.039 is less than the significance level of 0.05.
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The null hypothesis should be rejected. Since the p-value is less than the significance level, we reject the null hypothesis. This means that the proportion of students with student loan debt at Dr. Blackman's university does not equal 69%.
The statements that the results were not statistically significant, the null hypothesis should be accepted, and the null hypothesis cannot be rejected are incorrect based on the given p-value and significance level.
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