Question

Becoming more interested in what students do with their free time, a researcher collects several different samples of students and also notes the gender of the student. The results are below. Test to see whether or not activity is independent of gender at an alpha level of .01.

	Movie	Party	Dancing	Dinner	Tv	Reading	Other
Males	65	82	81	24	30	41	27
Females	12	55	30	12	30	48	33

Answer 1

State the hypothesis
H0: activity is independent of gender

H1: activity is not independent of gender

Observed Frequencies

	B1	B2	B3	B4	B5	B6	B7	Total
A1	65	82	81	24	30	41	27	350
A2	12	55	30	12	30	48	33	220
Total	77	137	111	36	60	89	60	570

Expected Frequencies

	B1	B2	B3	B4	B5	B6	B7	Total
A1	47.2807	84.1228	68.1579	22.1053	36.8421	54.6491	36.8421	350
A2	29.7193	52.8772	42.8421	13.8947	23.1579	34.3509	23.1579	220
Total	77	137	111	36	60	89	60	570

  Compute Chi-square

Chi square = 42.9707

Compute the degrees of freedom (df).
df=(2-1)⋅(7-1)=6

P value

for 6 df, p(χ2≥42.9707)=0

Decision :

Since the p-value(0) < α(0.01)

we reject the null hypothesis H0.

Conclusion :

alpha = 0.01 L.O.S there is no enough evidennce to claim that  activity is independent of gender .