Question

Professor McKee surveys his class about what they like to do on Sunday afternoons. 40 students say they like to watch TV, 30 say they like to exercise outdoors, and 40 say they like to eat ice cream. Test the hypothesis that students are actually indifferent between the three activities.

A) There is not enough information to test the hypothesis.
B) Students prefer watching TV over exercising outdoors.
C) Students are indifferent between the three activities.
D) Students prefer eating ice cream over watching TV.

Answer 1

To test if students have no preference for watching TV, exercising outdoors, or eating ice cream, a Chi-Square Goodness of Fit test is appropriate. However, there is not enough information provided to conduct the test fully, because we do not know the total number of students surveyed or if each activity preference is mutually exclusive.

Step-by-step explanation:

To test the hypothesis that students are actually indifferent between the three activities: watching TV, exercising outdoors, and eating ice cream, a Chi-Square Goodness of Fit test could be used. This test compares the observed frequencies with the expected frequencies if the null hypothesis (that students are indifferent between the activities) were true.

In this scenario, Professor McKee discovers that 40 students like to watch TV, 30 like to exercise outdoors, and 40 like to eat ice cream. Assuming that we have no preference for any activity, the expected frequency for each activity if students were truly indifferent would be the total number of students divided by the number of activities, which in this case is (40+30+40)/3 = 110/3 = 36.67.

However, given the provided information, we cannot conduct the hypothesis test without knowing the total number of students surveyed (as some students could like more than one activity) or if each response is mutually exclusive. Therefore, the correct answer is A) There is not enough information to test the hypothesis.