Question

	No Exercise	Exercise	Total
Campus Dormitory	32	58	90
On-Campus Apartment	74	106	180
Off –Campus Apartment	110	40	150
At Home	39	11	50
Total	255	215	470

You have now decided to collapse your data into on-campus and off-campus living (use data from #7) 2x2 table. Determine if there is a difference between living on-campus or off-campus and exercise status (yes exercise, no exercise).

1. state the null and alternative hypothesis

2. determine a

3. select chi square tool

4. Fine the critical value

5. reject or fail to reject

6. State the conclusion

Answer 1

Assume the level of significance to be 5%.

Chi-Square Independence test - Results

(1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: H0​: The two variables - living on-campus or off-campus and exercise status are independent Ha​: The two variables - living on-campus or off-campus and exercise status are dependent This corresponds to a Chi-Square test of independence. (2) Degrees of Freedom The number of degrees of freedom is df = (4 - 1) * (2 - 1) = 3 (3) Critical value and Rejection Region Based on the information provided, the significance level is α=0.05, the number of degrees of freedom is df = (4 - 1) * (2 - 1) = 3, so the critical value is 7.8147. Then the rejection region for this test becomes R={χ2:χ2>7.8147}. (4)Test Statistics The Chi-Squared statistic is computed as follows: (5)P-value The corresponding p-value for the test is p=Pr(χ2​>58.5666)=0 (6)The decision about the null hypothesis Since it is observed that χ2=58.5666>χ2_c​rit=7.8147, it is then concluded that the null hypothesis is rejected. (7)Conclusion It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the two variables - living on-campus or off-campus and exercise status are dependent, at the 0.05 significance level. Conditions: a. The sampling method is simple random sampling. b. The data in the cells should be counts/frequencies c. The levels (or categories) of the variables are mutually exclusive.