Problem 1 - EXAMPLE: p-value calculation for two-tailed z-test Problem statement and solution: 2.3. Suppose that we are testing Ho: =o versus H: o. Calculate the P-value for the following observed values of the test statistic: Zo=2.25 P-value = 0.02445 Solution manually calculated as 2* (0.5-0.4878)=0.0244 In MINITAB: Calc >> Probability Distributions >> Normal then get cumulative probability for the value 2.25 (entered in a cell in a worksheet) 0.987776 Then use Calc >> Calculator to calculate 2*(1-0.987776) 0.024448 Problem 2: p-value calculation for one-tailed z-test 2.4. Suppose that we are testing Ho: =o versus H: >. Calculate the P-value for the following observed values of the test statistic: (a) Z = 2.45 Manually: P-value = 0.00714 MINITAB: Problem 3: p-value calculation for two-tailed t-test 2.6. Suppose that we are testing Hou = versus H: with a sample size of n = n = 12. Both sample variances are unknown but assumed equal. Find bounds on the P-value for the following observed values of the test statistic: (a) t = 2.30 Manually: Table P-value = 0.02, 0.05 Computer P-value = 0.0313 MINITAB: Problem 4: p-value calculation for one-tailed t-test 2.7. Suppose that we are testing Ho M = versus H>M with a sample size of n = n = 10. Both sample variances are unknown but assumed equal. Find bounds on the P-value for the following observed values of the test statistic: (a) to = 2.31 Table P-value = 0.01, 0.025 Computer P-value = 0.01648 Solution Manually: MINITAB: Problem 5: p-value calculation for ANOVA F-test 3.1. An experimenter has conducted a single-factor experiment with four levels of the factor, and each factor level has been replicated six times. The computed value of the F-statistic is Fo = 3.26. Find bounds on the P-value. Table P-value = 0.025, 0.050 Computer P-value = 0.043 Manually: MINITAB: