Question

Question Completion Status: QUESTION 8 Aspirin and heart attacks in Sweden. A Swedish study used 1360 patients who had suffered a stroke. Each patient was assigned to either aspirin treatment or placebo treatment. Patients were followed for 3 years and the number of deaths due to heart attacks was determined for each group. Sample 1: (placebo group): n=684; number of deaths due to heart attacks-29 Sample 2: (aspirin group) n=676; number of deaths due to heart attacks-18 a. Calculate and interpret the difference of proportions. (4 points) b. Calculate the confidence interval for the difference of proportions (2 points). c. State a null hypothesis and a two-tailed alternative hypothesis for the difference of proportions (4 points). d. Calculate the test statistic (z) for the difference of proportions (4 points) e. Based on your answers to parts a and b, is there a statistically significant difference in the proportion of deaths due to heart attack for those taking placebo versus aspirin? Explain your answer (2 points)

Answer 1

Excel add-in (Mega Stat) procedure: Step 1: In EXCEL, Select Add-Ins > Mega Stat > Hypothesis Tests. Step 2: Choose Proportion vs. Hypothesized Value. Step 3: Choose Data Input. Step 4: In Group 1, enter the value 29 under x and enter the value 684 under n. Step 5: In Group 2, enter the value 18 under x and enter the value 676 under n. Step 6: Enter 0 Under Hypothesized difference. Step 7: Choose not equal in alternative Step 8: Click OK. Excel add-in (Mega Stat) output:

Hypothesis test for two independent proportions p1 0.0424 29/684 p2 0.0266 18/676 18. 676 po 0.0346 p (as decimal) 47/1360 p (as fraction) 47. X 1360 n 684 0.0158 difference 0. hypothesized difference 0.0099 std. error 1.59 z .1114 p-value (two-tailed) -0.0036 confidence interval 95.% lower 0.0351 confidence interval 95.% upper 0.0194 margin of error The difference of proportions is hi - 2 = 0.0158. Interpretation: There is a positive difference between the proportions.

The 95% confidence interval for the difference of proportions is -0.0036<P.-<0.0351. Null hypothesis: Ho: P.-P2 = 0 There is no difference between the two proportions. Alternative hypothesis: H-P1-P270 There is a difference between the two proportions. The value of test statistic is z =1.59.

No, there is no statistically significant difference in the proportion of deaths due to heart attack for those taking placebo versus aspirin. Because the difference of proportions 0 lies inside the confidence interval.