Since an instant replay system for tennis was introduced at a major tournament,
ID: 3326818 • Letter: S
Question
Since an instant replay system for tennis was introduced at a major tournament, men challenged 1403 referee calls, with the result that 429 of the calls were overturned. Women challenged 764 referee calls, and 213 of the calls were overturned. Use a 0.01 significance level to test the claim that men and women have equal success in challenging calls.
Complete parts (a) through (c) below.
a. Test the claim using a hypothesis test. Consider the first sample to be the sample of male tennis players who challenged referee calls and the second sample to be the sample of female tennis players who challenged referee calls. What are the null and alternative hypotheses for the hypothesis test?
b. z=
c. p=
Explanation / Answer
Solution:-
pMale = 429/1403 = 0.3058
pFemale = 213/764 = 0.2788
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: P1 = P2
Alternative hypothesis: P1 P2
Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the proportion from population 1 is too big or if it is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a two-proportion z-test.
Analyze sample data. Using sample data, we calculate the pooled sample proportion (p) and the standard error (SE). Using those measures, we compute the z-score test statistic (z).
p = (p1 * n1 + p2 * n2) / (n1 + n2)
p = 0.2963
SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] }
SE = 0.02053
z = (p1 - p2) / SE
z = 1.31
where p1 is the sample proportion in sample 1, where p2 is the sample proportion in sample 2, n1 is the size of sample 1, and n2 is the size of sample 2.
Since we have a two-tailed test, the P-value is the probability that the z-score is less than - 1.31 or greater than 1.31.
Thus, the P-value = 0.1902
Interpret results. Since the P-value (0.1902) is greater than the significance level (0.05), we have to accept the null hypothesis.
From the above test we have sufficient evidence in the favor of the claim that men and women have equal success in challenging calls.