Question

A high school wanted to know if the proportion of students who request virtual classes, in-person classes, or to skip a year was different at two different campuses. At each campus, they took a random sample of 100 students and asked each student which type of class they preferred. The chi-square test statistic for the test was calculated to be 5.21 with an associated p-value of 0.0857. If the significance level of the test was α = 0.05, what conclusion should they make about the proportion of students who request virtual classes, in-person classes, or to skip a year at two different campuses?

A. There is a significant difference in proportions between the two campuses.
B. There is no significant difference in proportions between the two campuses.
C. The test results are inconclusive.
D. More information is needed to make a conclusion.

Answer 1

Since the chi-square test's p-value (0.0857) is greater than the significance level of 0.05, we do not reject the null hypothesis, implying no significant difference in student preferences between two campuses.

Step-by-step explanation:

Given the chi-square test statistic of 5.21 with a p-value of 0.0857, and a significance level (α) of 0.05, we can make a conclusion regarding the proportion of students who request different types of classes at two different campuses. Since the p-value is greater than the α value (0.0857 > 0.05), we do not reject the null hypothesis. This means there is no sufficient statistical evidence to conclude that there is a significant difference in proportions between the two campuses regarding requests for virtual classes, in-person classes, or to skip a year. Therefore, the correct conclusion is B. There is no significant difference in proportions between the two campuses.