Question

Qualifications of male and female head and assistant college athletic coaches were compared in an article. Each person in random samples of 2217 male coaches and 1157 female coaches was classified according to number of years of coaching experience to obtain the accompanying two-way table. Is there enough evidence to conclude that the proportions falling into the experience categories are different for men and women? Use ? = 0.01.

Years of Experience
Gender	1–3	4–6	7–9	10–12	13+
Male	196	370	481	364	806
Female	233	255	239	167	263

a) Calculate the test statistic. (Round your answer to two decimal places.) ?² =

Answer 1

The following cross tablulation have been provided. The row and column total have been calculated and they are shown below:

	Male	Female	Total
1 - 3	196	233	429
4 - 6	370	255	625
7 - 9	481	239	720
10 - 12	364	167	531
13+	806	263	1069
Total	2217	1157	3374

Expected Values	Column 1	Column 2	Total
Row 1	2217*429/3374 = 281.889	1157*429/3374 = 147.111	429
Row 2	2217*625/3374 = 410.677	1157*625/3374 = 214.323	625
Row 3	2217*720/3374 = 473.1	1157*720/3374 = 246.9	720
Row 4	2217*531/3374 = 348.911	1157*531/3374 = 182.089	531
Row 5	2217*1069/3374 = 702.422	1157*1069/3374 = 366.578	1069
Total	2217	1157	3374

?2 = 134.89