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) TV watching is preferred over exercise and ice cream.
b) Students are indifferent between watching TV, exercising outdoors, and eating ice cream.
c) Exercising outdoors is the most preferred activity.
d) Eating ice cream is the least preferred activity.

Answer 1

To test the hypothesis that students are actually indifferent between the three activities (TV watching, exercising outdoors, and eating ice cream), we need to perform a chi-square test of independence.

Step-by-step explanation:

To test the hypothesis that students are actually indifferent between the three activities (TV watching, exercising outdoors, and eating ice cream), we need to perform a chi-square test of independence. The null hypothesis is that the activities are independent, while the alternative is that there is a preference for one activity over the others.

To conduct the test, we need to create a contingency table with the observed frequencies. Let's say we have three categories: A (TV watching), B (exercise), and C (ice cream). Based on the survey results, we have 40 students who like TV, 30 students who like exercise, and 40 students who like ice cream.

Once we have the contingency table, we can calculate the expected frequencies assuming independence. We sum the row and column totals to find the expected frequency for each cell. After that, we use the chi-square formula to calculate the chi-square test statistic, which measures the difference between the observed and expected frequencies. Finally, we compare the test statistic to the critical value from the chi-square distribution to determine if we reject or fail to reject the null hypothesis.