## MS Mod 8 Difference in population proportions practice exam questions

 Author Message NEAS Supreme Being         Group: Administrators Posts: 4.2K, Visits: 1.2K MS Module 8 Difference in population proportions practice exam questions(The attached PDF file has better formatting.)A study on a treatment group vs a control group shows    treatment    controlobservations    60    89successes    41    60●    The null hypothesis is H0: p1 = p2, where p1 and p2 are the true proportions of success for the two groups.●    The alternative hypothesis is Ha: p1 ≠ p2.●    The difference in population proportions is the proportion of successes for the treatment group minus the proportion of successes for the control group.Question 1.2: Sample difference in the proportions of successWhat is the sample difference in the proportions of success between the two groups?Answer 1.2: 41 / 60 – 60 / 89 = 0.0092Question 1.3: Proportion of success in combined sampleWhat is the sample proportion of success in the combination of the two groups?Answer 1.3: (41 + 60) / (60 + 89) = 0.6779(total successes / total observations) Question 1.4: Variance of the sample differenceWhat is the variance of the sample difference in the proportions of success between the two groups if the null hypothesis is true?Answer 1.4: (0.6779 × (1 – 0.6779) ) × (1 / 60 + 1 / 89) = 0.006093(if null hypothesis is true, use the combined proportion of success for each group)Question 1.5: Standard deviation of the sample differenceWhat is the standard deviation of the sample difference in the proportions of success between the two groups if the null hypothesis is true?Answer 1.5: 0.0060930.5 = 0.0781(standard deviation = square root of variance) Question 1.6: Z statistic What is the z statistic to test the null hypothesis H0: p1 = p2?Answer 1.6: 0.0092 / 0.0781 = 0.1178(z statistic = difference in proportions / standard deviation of this difference)Question 1.7: p valueWhat is the p value for the two-tailed z test of the null hypothesis H0: p1 = p2?Answer 1.7: 2 × Φ(-0.1178) = 0.9062Interpolating in the statistical tables: Φ(0.11) = 0.5438Φ(0.12) = 0.5478Φ(0.1178) = ( (0.1178 – 0.11) × 0.5478 + (0.12 – 0.1178) × 0.5438) / (0.12 – 0.11) = 0.54692 × Φ(-0.1178) = 2 × (1 – 0.5469) = 0.9062 Attachments MS Module 8 Difference in population proportions practice exam questions.pdf (230 views, 45.00 KB) Edited 2 Years Ago by NEAS
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