Question

Please type the answer by computer

A university classifies faculty by rank as instructors, assistant professors, associate professors, and full professors. The data, by faculty rank and gender, are given in the following contingency table. Test to see if faculty rank and gender are independent.

FACULTY	instructor	assistant prof	associate prof	full prof
male	62	238	185	115
famle	118	122	123	37

Answer 1

Claim: Faculty rank and gender are independent.

The null and alternative hypothesis is

H0: Faculty rank and gender are independent.

H1: Faculty rank and gender are not independent.

Level of significance = 0.05

Test statistic is

O: Observed frequency
E: Expected frequency.
E = ( Row total*Column total) / Grand total

FACULTY	instructor	assistant prof	associate prof	full prof	Total
male	62	238	185	115	600
famle	118	122	123	37	400
Total	180	360	308	152	1000

O	E	(O-E)	(O-E)^2	(O-E)^2/E
62	108	-46	2116	19.59259
238	216	22	484	2.240741
185	184.8	0.2	0.04	0.000216
115	91.2	23.8	566.44	6.210965
118	72	46	2116	29.38889
122	144	-22	484	3.361111
123	123.2	-0.2	0.04	0.000325
37	60.8	-23.8	566.44	9.316447
			Total	70.11

Degrees of freedom = ( Number of rows - 1 ) * ( Number of column - 1) = ( 2 - 1) * (4 - 1) = 1 * 3 = 3
Critical value = 7.815

( From chi-square table)

Test statistic > critical value we reject null hypothesis.

Conclusion:

Faculty rank and gender are not independent.