Student-athletes and gambling. A survey of student-athletes that asked questions about gambling behavior classified students according to the National Collegiate Athletic Association (NCAA) division. The percents of male student-athletes who reported wagering on collegiate sports are given here along with the numbers of respondents in each division:
(a) Use a significance test to compare the percents for the three NCAA divisions. Give details and a short summary of your conclusion.
(b) The percents in the preceding table are given in the NCAA report, but the numbers of male student-athletes in each division who responded to the survey question are estimated based on other information in the report. To what extent do you think this has an effect on the results?
(c) Some student-athletes may be reluctant to provide this kind of information, even in a survey where there is no possibility that they can be identified. Discuss how this fact may affect your conclusions.
(d) The chi-square test for this set of data assumes that the responses of the student-athletes are independent. However, some of the students are at the same school and even on the same team. Discuss how you think this might affect the results.