Question

Students in a statistics class were asked which of three lifetime achievements they would most like to win: a Nobel Prize, an Academy Award, or an Olympic Gold Medal. They were also asked to indicate their gender. Results are shown in the following table: Female Male Nobel Prize 12 5 Academy Award 8 2 Olympic Gold Medal 10 18 Suppose that you were to conduct a chi-square test on these data. 1. State the appropriate null hypothesis in words. 2. Determine the expected count for women who would choose a Nobel Prize. 3. Report the value that you would you use for degrees of freedom with this test. 4. If the p-value turned out to be very small, what conclusion (in context) would you draw? 5. Even if this were a random sample from the population of all students at the university, one of the technical conditions of the chi-square test would still not be satisfied with these data. Explain.

Answer 1

(1)

H0: Null Hypothesis: Lifetime achievents to win: a Nobel Prize, an Academy Award or an Olympic Awars is independent of Gender.

(2)

                           Female                 Male                       Total

Nobal prize               12                     5                            17

Academy Award         8                     2                            10

Olympic Gold Medal   10                   18                            28

Total                           30                 25                              55

The Expected count for women who would choose a Nobel Prize = 12

3. Degrees of freedom = (3 - 1) X (2 - 1) = 2

4. If p- value turned out to be very small, the conclusion is: Reject the Null Hypothesis. Lifetime Achievements to win: a Nobel Prize, an Academy Award or an Olympic Gold Medal is dependent on Gender.

5.

Assuming H0, the Expected Frequencies are got as follows:

                           Female              Male            Total

Nobel Prize      30X17/55=9.27       7.73               17

Academic Award     5.45                 4.55              10

Olympic Gild Medal 15.27               12.73             28

Total                        30                     25               55

One of the Expected Frequencies is 4.55, which is less than 5. Thus, One of the technical conditions of the chi square test: All the Expected frequencies should be greater than 5, would not be satisfied with these data.