Question

Gender and College Students: According to the U.S. Department of Education, approximately 57% of students attending colleges in the U.S. are female. A statistics student is curious whether this is true at her college. She tests the hypotheses H0: p 0.57 versus Ha: p #0.57. The P-value is not small enough to reject the null hypothesis. Which of the following is an appropriate conclusion?

a. The probability that the proportion of female students at the college is different from 0.57 is equal to the level of significance, 0.05.
b. There is enough evidence to say that the proportion of female students at the college is different from 0.57
c. There is enough evidence to say that the proportion of female students at the college is equal to the national figure of 57%.
d. There is not enoughevidence to say that the proportion of female students at the college is different from 0.57

Answer 1

The correct conclusion is that there is not enough evidence to say that the proportion of female students at the college is different from 0.57. The decision to not reject the null hypothesis is based on the p-value being greater than the significance level (alpha).

Step-by-step explanation:

The student is working with hypothesis testing to determine if the proportion of female students at her college is different from the national average of 57%. In hypothesis testing, the null hypothesis H0 represents a default position that there is no difference between a specific sample and the population parameter. Here, H0: p = 0.57 versus Ha: p ≠ 0.57, where p is the true proportion of female students at the student's college.

When analyzing hypothesis tests, we compare the p-value to the significance level, often designated as alpha (α). If the p-value is less than alpha, there is enough evidence to reject the null hypothesis and accept the alternative hypothesis. Conversely, if the p-value is greater than alpha, we do not reject the null hypothesis.

In this case, because the question explicitly states that the p-value is not small enough to reject the null hypothesis, the correct conclusion is option d: "There is not enough evidence to say that the proportion of female students at the college is different from 0.57." Any other options suggesting that there is enough evidence to either affirm or deny the proportion of female students would be incorrect given the context provided.