Inferences with Two Proportions Access tech supplements, videos, and data sets at www.TriolaStats.com TECH CENTER continued R R command: prop.test(x, y, alternative=c(“two.sided”, “less”, “greater”), conf.level=0.95, correct=FALSE) where x is a vector of successes in group 1 and 2 and y is a vector of the sample sizes of group 1 and 2. TIP: The results include the x2 (X-squared) statistic. The z-statistic can be found by taking the square root of the x2 statistic. TIP: For Example 1: prop.test(x, y, alternative=“two. sided”, conf.level=0.95, correct=FALSE2; where x=c179,442 and y=c1438,4462. A complete list of R statistical commands is available at TriolaStats.com Excel XLSTAT Add-In (Required) 1. Click on the XLSTAT tab in the Ribbon and then click Parametric tests. 2. Select Tests for two proportions from the dropdown menu. 3. Under Data Format select Frequencies if you know the number of successes x or select Proportions if you know the sample proportion pn. 4. Enter the frequency or sample proportion and sample size for both samples. 5. Check z test, uncheck Continuity Correction, and uncheck Monte Carlo method. 6. Click the Options tab. 7. Hypothesis Testing: Under Alternative hypothesis select the desired format (3 for two-tailed test, * for left-tailed test, + for right-tailed test). For Hypothesized difference enter 0. Enter the desired significance level (enter 5 for 0.05 significance level). Under Variance select pq11,n1 + 1,n22. Confidence Intervals: Under Alternative hypothesis select 3 D for a two-tailed test. For Hypothesized difference enter 0. Enter the desired significance level (enter 5 for a 95% confidence level). Under Variance select p1q1,n1 + p2q2,n2. 8. Click OK to display the results that include the test statistic labeled z(Observed value), P-value, and confidence interval. 9-1 Two Proportions 449 Statistical Literacy and Critical Thinking 1.Salk Vaccine: Verifying Requirements In the largest clinical trial ever conducted, 401,974 children were randomly assigned to two groups. The treatment group consisted of 201,229 children given the Salk vaccine for polio, and 33 of those children developed polio. The other 200,745 children were given a placebo, and 115 of those children developed polio. If we want to use the methods of this section to test the claim that the rate of polio is less for children given the Salk vaccine, are the requirements for a hypothesis test satisfied? Explain. 2. Notation For the sample data given in Exercise 1, consider the Salk vaccine treatment group to be the first sample. Identify the values of n1, p n 1, q n 1, n2, p n 2, q n 2, p, and q. Round all values so that they have six significant digits. 3.Hypotheses and Conclusions Refer to the hypothesis test described in Exercise 1. a. Identify the null hypothesis and the alternative hypothesis. b. If the P-value for the test is reported as “less than 0.001,” what should we conclude about the original claim? 9-1 Basic Skills and Concepts
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