Lipitor is a drug used to control cholesterol. In clinical trials of Lipitor, 34

Question

Lipitor is a drug used to control cholesterol. In clinical trials of Lipitor, 340 subjects were treated with Lipitor and 200 subjects were given a placebo. Among those treated with Lipitor, 102 developed infections. Among those given a placebo, 46 developed infections. Test the claim that the rate of infection for those treated with Lipitor was more than rate of infection for those given a placebo. at the .025 significance level.

Claim: Select an answer u 1 u 2 u 1 = u 2 p 1 = p 2 u 1 u 2 u 1u 2 p 1 > p 2 p 1 p 2 u 1 > u 2 p 1 < p 2 u 1 < u 2 p 1 p 2 p 1p 2  which corresponds to Select an answer H1: u 1 > u 2 H0: p 1 p 2 H0: u 1 u 2 H1: u 1 < u 2 H0: p 1p 2 H0: p 1 = p 2 H1: u 1u 2 H1: p 1 < p 2 H1: p 1p 2 H1: p 1 > p 2  

Opposite: Select an answer p 1 p 2 p 1 < p 2 u 1 < u 2 u 1 u 2 p 1p 2 u 1u 2 u 1 = u 2 p 1 > p 2 u 1 u 2 u 1 > u 2 p 1 = p 2 p 1 p 2  which corresponds to Select an answer H0: u 1u 2 H1: u 1 = u 2 H1: u 1 u 2 H1: u 1 <= u 2 H0: p 1p 2 H1: p 1 > p 2 H0: p 1 p 2 H0: u 1 > u 2 H1: p 1 < p 2 H1: p 1p 2 H0: p 1 = p 2  


The test is:  Select an answer two-tailed right-tailed left-tailed  

The test statistic is: zz = Select an answer 1.76 1.54 2.06 1.92 2.25  

The critical value is: zz= Select an answer  1.96  2.2  2.15  2.09  1.46  

Based on this we: Select an answer Reject the null hypothesis Cannot determine anything Fail to reject the null hypothesis Accept the null hypothesis  

Conclusion There Select an answer does not does appear to be enough evidence to support the claim that the rate of infection for those treated with Lipitor was more than rate of infection for those given a placebo..

Explanation / Answer

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: P1< P2

Alternative hypothesis: P1 > P2

Note that these hypotheses constitute a one-tailed test.

Formulate an analysis plan. For this analysis, the significance level is 0.025. The test method is a two-proportion z-test.

Analyze sample data. Using sample data, we calculate the pooled sample proportion (p) and the standard error (SE). Using those measures, we compute the z-score test statistic (z).

p = (p1 * n1 + p2 * n2) / (n1 + n2)

p = 0.2741

SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] }

SE = 0.03975

z = (p1 - p2) / SE

z = 1.76

zcritical = 1.96

where p1 is the sample proportion in sample 1, where p2 is the sample proportion in sample 2, n1 is the size of sample 1, and n2 is the size of sample 2.

Since we have a one-tailed test, the P-value is the probability that the z-score is less than

Thus, the P-value = 0.0392

Interpret results. Since the P-value (0.0392) is greater than the significance level (0.025), we cannot reject the null hypothesis.

Fail to reject the null hypothesis

Conclusion There Select an answer does not does appear to be enough evidence to support the claim that the rate of infection for those treated with Lipitor was more than rate of infection for those given a placebo..

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