Question

Is attractiveness related to deciding to go out on a date?   Below is data for males and females from a study on speed dating

Male

	Decision
Attractiveness Rating	Date	No Date
0-4	11	0
4-8	100	65
8-10	16	81

Female

	Decision
Attractiveness Rating	Date	No Date
0-4	22	4
4-8	109	64
8-10	17	58

1. What type of hypothesis test would you use to see if attractiveness and deciding on a date are related for males?
a. Goodness of Fit
b. Test of Heterogeneity
c. Test of Independence

2. What type of hypothesis test would you use to see if attractiveness and deciding on a date are related for females?
a. Goodness of Fit
b. Test of Heterogeneity
c. Test of Independence

3. Can you conduct the tests with data as given?
a. Yes, because each cell has a positive number in it
b. Yes, because each cell has a large enough value
c. No, since totals are not given to us
d. No, since there cells with values less than five

4. Combine the lower two categories and conduct the tests. What are the p-values for the tests for
a. Males
b. Females

5. Are attractiveness and deciding on a date related?
a. No for males, No for females
b. No for males, Yes for females
c. Yes for males, No for females
d. Yes for males, Yes for females

Answer 1

1. Here, option (c) test for Independence should be conducted to determine if attractiveness and deciding on a date are related/dependent since we need to conduct chi-square test of Independence on a two-way table. For one-way table only, test for goodness of fit is conducted not for two-way tables.

2. Here also by the same logic, option (c) test for Independence is the correct option.

3. Option (b) yes, because every week has a large enough value since for chi-square test only one condition is needed i.e, expected value = row total * column total / total should be >= 5 and since here the values are quite high, this condition will be satisfied and hence chi-square can be conducted.