Use the sign test for the data consisting of matched pairs. Oscar Winners? Repeat Exercise using all of the 82 pairs of ages in Data Set 11 from Appendix B. For that data set, there are 16 positive signs, 64 negative signs, and 2 ties. Exercise Use the sign test for the data consisting of matched pairs. Oscar Winners?Listed below are ages of actresses and actors at the times that they won Oscars. These 10 matched pairs are the first 10 from Data Set 11 in Appendix B. The data are paired according to the years that they won. Use a 0.05 significance level to test the claim that there is no difference between the ages of best actresses and the ages of best actors at the time that the awards were presented.

Solution 10BSC Step 1 By using = 0.05 level of significance t o test the claim that there is no difference between the ages of best actresses and the ages of best actors at the time that the awards were presented. The Hypotheses can be expressed as H0 There is no difference between the ages of best actresses and the ages of best actors at the time that the awards were presented. H : There is a difference between the ages of best actresses and the ages of best actors at 1 the time that the awards were presented. We know that, Positive signs = 16 Negative signs = 64 Number of ties = 2 Now, the Test Statistic is the less frequent sign i.e., positive sign = 16 Therefore, x = 16 is the required value of test statistic. Hence for sign test the required sample size used is 80 i.e., n = 16 + 64 = 80 which is greater than 25 (n 25). Hence the Test Statistic x = 16 can be converted to the Test Statistic as shown below n (x + 0.5) 2 ( ) z = 2 (16 + 0.5) ) z = 80 2 2 On substitution we get, z = -5.26 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 = -5.26 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 the ages of best actresses and the ages of best actors at the time that the awards were presented.