13-2 Sign Test 651 z 5 0 Reject p 5 0.5 Fail to reject p 5 0.5 Sample data: z 5 –26.41 z 5 21.645 FIGURE 13-2 Testing Effectiveness of the XSORT Gender Selection Method H0: p = 0.5 1the proportion of girls is equal to 0.52 H1: p 7 0.5 1girls are more likely2 Denoting girls by positive signs 1+2 and boys by negative signs 1-2, we have 879 positive signs and 66 negative signs. Using the sign test procedure summarized in Figure 13-1, we let the test statistic x be the smaller of 879 and 66, so x = 66 boys. Instead of trying to determine whether 879 girls is high enough to be significantly high, we proceed with the equivalent goal of trying to determine whether 66 boys is low enough to be significantly low, so we treat the test as a left-tailed test. The sample data do not contradict the alternative hypothesis because the sample proportion of girls is 879> 945, or 0.930, which is greater than 0.5, as in the above alternative hypothesis. Continuing with the procedure in Figure 13-1, we note that the value of n = 945 is greater than 25, so the test statistic x = 66 is converted (using a correction for continuity) to the test statistic z as follows: z = 1x + 0.52 - a n 2b 2 n 2 = 166 + 0.52 - a 945 2 b 2 945 2 = -26.41 P-Value We could use the test statistic of z = -26.41 to find the left-tailed P-value of 0.0000 (Table: 0.0001). That low P-value causes us to reject the null hypothesis. Critical Value With a = 0.05 in a left-tailed test, the critical value is z = -1.645. Figure 13-2 shows that the test statistic z = -26.41 is in the critical region bounded by z = -1.645, so we reject the null hypothesis that the proportion of girls is equal to 0.5. There is sufficient sample evidence to support the claim that girls are more likely with the XSORT method. YOUR TURN. Do Exercise 9 “Buttered Toast Drop Test.” INTERPRETATION The XSORT method of gender selection does appear to be associated with an increase in the likelihood of a girl, so this method appears to be effective (but this hypothesis test does not prove that the XSORT method is the cause of the increase).
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