Question

The accompanying table shows results of challenged referee calls in a major tennis tournament. Use a 0.05 significance level to test the claim that the gender of the tennis player is independent of whether a call is overturned.

Was the Challenge to the Call Successful?

	Yes	No
Men	393	771
Women	282	913

Answer 1

The Observed and expected values are as below. Each Expected value = Row Total * Column Total / N

Observed
	Yes	No	Total
Men	393	771	1164
Women	282	913	1195
Total	675	1684	2359
Expected
	Yes	No	Total
Men	333.06	830.94	1164
Women	341.94	853.06	1195
Total	675	1684	2359

The Hypothesis:

H0: There is no relation between gender and whether a call is overturned.

Ha: There is a relation between gender and whether a call is overturned.

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(b) The Test Statistic:

Number	Observed	Expected	(O-E)	(O-E)2	(O-E)2/E
1	393	333.06	59.94	3592.221248	10.7854
2	282	341.94	-59.94	3592.221248	10.5056
3	771	830.94	-59.94	3592.221248	4.3231
4	913	853.06	59.94	3592.221248	4.2110
Total					29.825

as found above = 29.825

The degrees of freedom, df = (r – 1) * (c -1) = (2 - 1) * (2 - 1) = 1 * 1 = 1

(d) The Critical Value:   The critical value at = 0.05, df = 1

critical = 3.8415

(e) The p value: The p value at = 29.825, df = 1, is P value = 0000.

The Decision Rule: If test is > critical, then Reject H0.

If p value is < , Then Reject H0.

The Decision: Since test (29.825) is > critical (3.8415), We Reject H0.

Since p value (0.000) is < (0.05), We Reject H0.

The Conclusion: There is sufficient evidence at the 95% significance level to conclude that there is a relation between gender and whether a call is overturned.

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