Inferences with Two Means: Matched Pairs Access tech supplements, videos, and data sets at www.TriolaStats.com TECH CENTER continued R R command: t.test(x, y, alternative=c(“two.sided”, “less”, “greater”), paired=TRUE, conf.level=0.95) where x and y are each vectors of matched pairs of sample data. TIP: For Example 1: t.test(x, y, alternative=“greater”, paired=TRUE, conf.level=0.95) A complete list of R statistical commands is available at TriolaStats.com Statistical Literacy and Critical Thinking 1.Is Friday the 13th Unlucky? Listed below are numbers of hospital admissions in one region due to traffic accidents on different Fridays falling on the 6th day of a month and the following 13th day of the month (based on data from “Is Friday the 13th Bad for Your Health,” by Scanlon et al., British Medical Journal, Vol. 307). Assume that we want to use a 0.05 significance level to test the claim that the data support the claim that fewer hospital admissions due to traffic accidents occur on Friday the 6th than on the following Friday the 13th. Identify the null hypothesis and alternative hypothesis. Friday 6th 9 6 11 11 3 5 Friday 13th 13121410 4 12 2.Friday the 13th Refer to the sample data from Exercise 1. a. Find the differences d, then find the values of d and sd. b. In general, what does md represent? 3.Confidence Interval Assume that we want to use the sample data in Exercise 1 for constructing a confidence interval to be used for testing the given claim. a. What is the confidence level that should be used for the confidence interval? b. What is the critical t value that should be used for finding the margin of error E? c. If the resulting confidence interval is -5.8 admissions 6 md 6 -0.9 admissions, what do you conclude? 4.True or False For the methods of this section, determine whether the following statements are true or false. a. When testing a claim with matched pairs of data, hypothesis tests using the P-value method, critical value method, and confidence interval method will all result in the same conclusion. b. If a simple random sample of 50 matched pairs of data yields differences with a distribution that is far from normal, then the methods of this section should not be used. c. The methods of this section can be used with pulse rates of 100 randomly selected adult women and 100 randomly selected adult men. d. If using the methods of this section to test a claim that md ≠ 0 and it is found that the 95% confidence interval does not include 0, then the P-value must be 0.05 or less. e. If the methods of this section are used with pulse rates of 100 subjects before and after exercise, the sample size is n = 200. 9-3 Basic Skills and Concepts 476 CHAPTER 9 Inferences from Two Samples
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