Assume that matched pairs of data result in the given number of signs when the value of the second variable is subtracted from the corresponding value of the first variable. Use the sign test with a 0.05 significance level to test the null hypothesis of no difference. Positive signs: 172; negative signs: 439; ties: 0 (from challenges to referee calls in the most recent U.S. Open tennis tournament)

Solution 8BSC Step 1 By assuming that matched pairs of data result in the given number of signs when the value of the second variable is subtracted from the corresponding value of the first variable. We use the sign test with a 0.05 significance level to test the null hypothesis of no difference. The Hypotheses can be expressed as H0 There is no difference between challenges to referee calls in the most recent U.S. Open tennis tournament. H1 There is a difference between challenges to referee calls in the most recent U.S. Open tennis tournament. We know that, Positive signs = 172 Negative signs = 439 Number of ties = 0 Now, the Test Statistic is the less frequent sign i.e., positive sign = 172 Therefore, x = 172 is the required value of test statistic. Hence for sign test the required sample size used is 611 i.e., n = 172 + 439 = 611 which is greater than 25 (n 25). Hence the Test Statistic x = 172 can be converted to the Test Statistic as shown below (x + 0.5) 2 ( ) z = n (172 + 0.5) ) z = 611 2 2 On substitution we get, z = -10.76 From A-2 table, the critical values are z = -1.96 and z = 1.96 for two tailed test. Hence the critical region is (z -1.96)(z 1.96) From the above figure, we see that z = -10.76 does not fall within the critical region. Hence we reject the Null hypothesis and conclude that there is a sufficient evidence to claim that There is a difference between challenges to referee calls in the most recent U.S. Open tennis tournament.