Question

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

Male

	Decision
Intelligence Rating	Date	No Date
0-8	66	53
8-10	58	91

Females

	Decision
Intelligence Rating	Date	No Date
0-8	57	34
8-10	90	92

1. What type of hypothesis test would you use to see if intelligence 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 intelligence 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. What are the p-values for the tests for
a. Males
b. Females

5. Are intelligence 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

Ans:

1) Test of Independence

2) Test of Independence

3)Yes, because each cell has a large enough value(expected count>5)

4)Males:

	Observed count(fo)
Intelligence	Date	No Date
Rating			Total
0-8	66	53	119
8-10	58	91	149
Total=	124	144	268
	Expected count(fe)
Intelligence	Date	No Date
Rating			Total
0-8	55.06	63.94	119
8-10	68.94	80.06	149
Total=	124	144	268
	chi square=(fo-fe)^2/fe
Intelligence	Date	No Date
Rating			Total
0-8	2.17	1.87	4.05
8-10	1.74	1.50	3.23
Total=	3.91	3.37	7.28

Test statistic:

Chi square score=7.28

df=(2-1)*(2-1)=1

p-value=CHIDIST(7.28,1)=0.0070

Females:

	Observed count(fo)
Intelligence	Date	No Date
Rating			Total
0-8	57	34	91
8-10	90	92	182
Total=	147	126	273
	Expected count(fe)
Intelligence	Date	No Date
Rating			Total
0-8	49.00	42.00	91
8-10	98.00	84.00	182
Total=	147	126	273
	chi square=(fo-fe)^2/fe
Intelligence	Date	No Date
Rating			Total
0-8	1.31	1.52	2.83
8-10	0.65	0.76	1.41
Total=	1.96	2.29	4.24

Test statistic:

Chi square score=4.24

df=(2-1)*(2-1)=1

p-value=CHIDIST(4.24,1)=0.0394

5)Assume significance level=0.05

For,Males:

As,p-value<0.05,we reject null hypothesis and we can conclude that intelligence and deciding on a date are related.

For,Females:

As,p-value<0.05,we reject null hypothesis and we can conclude that intelligence and deciding on a date are related.

So,option d is correct.(Yes for males, Yes for females)