Question

U Question 8 3 pts Lipitor (atorvastatin) is a drug used to control cholesterol. In clinical trials of Lipitor, 94 subjects were treated with Lipitor and 270 subjects were given a placebo. Among those treated with Lipitor, 7 developed infections. Among those given a placebo, 27 developed infection. We want to use a 0.05 significance level to test the claim that the rate of infections was the same for those treated with Lipitor as those given a placebo. A What is the appropriate null hypothesis? i. Ho: PLigier Priacto = 0 ii. Ho: PLipior - Probo #0 iii. Ho: Pacebo- ptipltor = 0 iv. Ho: pPlaabe - Plipitor 0 v. None of the above. B. What is the test statistic? C. What are the critical value(s)? D What is the test statistic p-value? E. What is the Margin of Error, E? F. Construct the appropriate confidence interval to test the claim. G. What are your final conclusions? i. Reject the Null and conclude that the two groups have different rates of infection ii. Fail to Reject the Null and conclude that the two groups have the same rates of infection iii. Reject the Null and conclude that the two groups have the same rates of infection iv. Fail to Reject the Null and conclude that the two groups have different rates of infection v. None of the above.

Answer 1

For sample 1, we have that the sample size is N1 = 94, the number of favorable cases is Xı = 7, so then the sample proportion is pi = * = 51 = 0.0745 For sample 2, we have that the sample size is N2 = 270, the number of favorable cases is X2 27, so then the sample proportion is p2 = x3 = 2% = 0.1 The value of the pooled proportion is computed as p = X+X Ni+N2 7+27 94+270 0.0934 Also, the given significance level is a = 0.05. (1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: Ho: p1 = P2 Ha: px = = P2 This corresponds to a two-tailed test, for which a z-test for two population proportions needs to be conducted. (2) Rejection Region 0.05, and the Based on the information provided, the significance level is a = critical value for a two-tailed test is ze = 1.96. The rejection region for this two-tailed test is R= {z : |Z| > 1.96} .. (3) Test Statistics The z-statistic is computed as follows: 0.0745 – 0.1 z = P1 – P2 Võ(1 – 7)(1/nı + 1/n2) -0.733 0.0934 · (1 – 0.0934)(1/94 + 1/270) (4) Decision about the null hypothesis 0.733 < Zc 1.96, it is then concluded that the null Since it is observed that | || hypothesis is not rejected. 0.4638 Using the approach: The p-value is p = 0.4638, and since p 0.05, it is concluded that the null hypothesis is not rejected. (5) Conclusion It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population proportion p1 is different than P2, at the 0.05 significance level. Confidence Interval The 95% confidence interval for P1 – P2 is: -0.09 < P1 – P2 < 0.038.

Z-test for Two Proportions, z = -0.733, p = 0.4638 0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00 -4.0 -3.5 -3.0-2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

A) i

E) (0.038-(-0.09))/2

0.128/2

0.064

G) ii

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