Question

STAT 202 Assignment 3 A Swedish study used 1360 patients who had suffered from a stroke. The study randomly assigned each subject to an aspirin treatment or a placebo treatment. The contingency table shows the results of the study, where X is the number of deaths due to heart attack during a follow-up period of about 3 years. Sample 1 received the placebo and sample 2 received aspirin. 1. Group Placebo Aspirin 38 18 684 676 Find a 95% confidence interval for the difference in death rates for the two groups. Perform a hypothesis test to formally test if there is a difference in the proportions with a 0.05 level of significance. a. b. The specialty food chain wants to compare the change in sales across different regions. An examination of the difference in sales over a 37-week period in a recent year for 8 stores in the state of Pennsylvania compared to stores nearby states reveals the following descriptive statistics for relative increase in sales 2. State PA Other mean 0.0738 0.0559 Stdev 0.0666 0.0503 12 Assume variances of relative increases in sales in PA and in other states are equal; write the appropriate hypothesis to test whether there is a difference between relative increase in PA and other states, find the test statistics and p-value draw a conclusion at the 0.05 level of significance.

Answer 1

here,

forPlacebo:

n1 = 684 and p1 = 38 / 684 = 0.06

for aspirin :

n2 = 676 and p2 = 18 / 676 = 0.03

a) for 95% of CI, Z = 1.96 (Fro standard normal table)

so, 95% of CI = (p1 - p2) +/- Z * sqrt(p1(1-p1)/n1 + p2(1-p2)/n2)

= (0.06 - 0.03) +/- 1.96 * sqrt(0.06*(1-0.06)/684 + 0.03*(1-0.03)/676)

= 0.03 +/- 0.022

= (0.03 - 0.022 , 0.03 + 0.022)

= (0.008 , 0.052)

b) here

test hypothesis,

H0 : p1 = p2

Ha : p1 $\neq$ p2

therefore test statistic,

Z=(p1-p2)/√[p1*(1-p1)/n1 +p2*(1-p2)/n2]

=(0.06-0.03)/sqrt(0.06*(1-0.06)/684+ 0.03*(1-0.03)/676)

=2.68

here, alpha = 0.05, the critical value , Z = 1.96 (From standard normal table)

since, Z = 2.68 is greater that Z critical, we reject the null hypothesis H0.

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