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 : versus : . she plans to use a significance level of 0.05. she calculates her test statistic to be 1.42. using the applet (at the top of this checkpoint), what is the p‐value?

a. P-value = 0.156
b. P-value = 0.078
c. P-value = 0.922
d. P-value = 0.05

Answer 1

To determine the correct p-value from the test statistic of 1.42 at the 0.05 significance level, an applet is typically used. Depending on the nature of the hypothesis test, the p-value tells us whether to reject or not reject the null hypothesis.

Step-by-step explanation:

The question is about determining the p-value related to a hypothesis test about the proportion of female college students in a particular college. To answer the question, the test statistic is given as 1.42 for a test where the significance level, or alpha (α), is 0.05. An applet would typically be used to calculate the p-value from the test statistic.

Comparing the p-value to alpha is key in deciding whether to reject the null hypothesis. In general:

• If the p-value is less than alpha, the null hypothesis is rejected.
• If the p-value is greater than alpha, the null hypothesis is not rejected.

The options given for the p-value are: a. 0.156, b. 0.078, c. 0.922, and d. 0.05. Without the exact distribution or the direction of the alternative hypothesis, we cannot select the correct p-value from those options. However, if the alternative hypothesis is two-sided, the p-value associated with a test statistic of 1.42 and a significance level of 0.05 would be greater than 0.05, implying that the null hypothesis would not be rejected based on this information.