Question

4. Use the Pank Sumn Test comparing prices of Red Sox and White Soutickets. Red Sox: 12 14 12 12 20 25 20 18 25 16 White Sox: 10 % 14 22 19 11 17 a) a) State the Null Hypothesis: b) Compute the test-statistic b). c) Compute the P-value

Answer 1

Step1: To, test the two prices of tickets at the 5% level of significance by utilzing the Wilcoxon rank sum test. Step2: The null and alternative hypotheses are: There is significant difference between the prices of HO:7). = 172 red sox and white sox tickets. There is not significant difference between the prices of H:17,7772 red sox and white sox tickets, Step3: The level of significance is a=0.05. . Step 4: The test is two-tailed test. 0.05 2 2 = 0.025. 2 The table values of the normal distribution is obtained by utilizing the normal distribution function of the Excel2010 is =normsinv(probability) =normsinv (0.025) z = 20.025 2 20.02s = +1.959964

(b) Step5: The test statistic is of the Wilcoxon rank sum test. We need to combine the data from the two samples. The combined data must be arranged in order, and should rank each value. We must indicate the group Soxes Group Rank 8 white sox 1.5 8 white sox 1.5 10 white sox 3.0 11 white sox 4.0 12 Red sox 5.5 12 Red sox 5.5 14 Red sox 7.5 14 white sox 7.5 16 Red Sox 9.0 17 Red sox 10.5 17 white sox 10.5 18 Red sox 12.0 19 white sox 13.0 20 Red Sox 14.5 20 Red sox 14.5 22 white sox 16.0 25 Red sox 17.5 25 Red sox 17.5 Since, the sample sizes are not equal. We can use the smaller sample size is to compute the sum of the ranks. R=8+8+10+11+14+17+19+22 109 R= 109

Step 6: The computation value of Hz n(n+n+1) 2 10(10+8+1) 2 10(19) 2 190 2 95 42 = 195 Therefore, the value of 4x is Hg = 195 The computation value of 0. (+2, +1) 12 (10) (8) (10+8+1) 12 (108)(19) 12 11520 12 V126.6667 11.25463 0, 11.254631 Therefore, the value of Ox is 0,- 11.25463 = The value of the z-test statistic is R-4x z= 109-95 11.25463 14 11.25463 1.243933 2 8 1.243933 Therefore, the value of the z- test statistic is zx 1.243933 (c) Step7: The p-value approach: P-value=2P (z >20) =2(1-P(z<zo)) =2(1-P(z <1.243933)) =2(1-0.893238) =2(0.106762) 0.213524 P-value = 0.2135 > a=0.05.

Step 8: The decision rule: If the test statistic isz > 2. We reject the null hypothesis Ho. Otherwise, we do not reject the null hypothesis Ho. Step9: The conclusion: Since, the test stati stic is z= 1.2439 <20025 = 1.9599 We do not reject the null hypothesis H, Since, the probability value is P-value = 0.2135 > a = 0.05. We do not reject the null hypothesis H,. The data do not provide sufficient evidence to conclude that there is significant difference between the prices of red sox and white sox tickets at the 5% level of significance.