REAL STATISTICS REAL DECISIONS Putting it all together 462 CHAPTER 8 Hypothesis Testing with Two Samples The U.S. Department of Health & Human Services (HHS) is a department of the U.S. federal government with the motto “Improving the health, safety, and well-being of America.” The Centers for Medicare & Medicaid Services work within the HHS to help administer Medicare, Medicaid, and other health programs. They also gather information about health expenditure, program utilization, and other data. One area studied is the average amount of time that Medicare patients spend at short-stay hospitals. You work for the Centers for Medicare & Medicaid Services. You want to test the claim that the mean length of stay for inpatients in 2019 is different than what it was in 2000 from a random sample of inpatient records. The results for several inpatients from 2000 and 2019 are shown in the histograms. EXERCISES 1. How Could You Do It? Explain how you could use each sampling technique to select the sample for the study. (a) stratified sample (b) cluster sample (c) systematic sample (d) simple random sample 2. Choosing a Sampling Technique (a) Which sampling technique in Exercise 1 would you choose to implement for the study? Why? (b) Identify possible flaws or biases in your study. 3. Choosing a Test To test the claim that there is a difference in the mean length of hospital stays, should you use a z@test or a t@test? Are the samples independent or dependent? Do you need to know what each population’s distribution is? Do you need to know anything about the population variances? 4. Testing a Mean Test the claim that there is a difference in the mean length of hospital stays for inpatients. Assume the populations are normal and the population variances are equal. Use a = 0.05. Interpret the test’s decision. Does the decision support the claim? 1 2 3 4 5 6 7 8 6 7 8 9 5 4 3 2 1 Frequency Length of stay (in days) Inpatients Length of Stay (2000) x f x1 = 6 n1 = 28 s1 ≈ 1.63 1 2 5 8 3 4 6 7 9 1 3 5 7 9 Frequency Length of stay (in days) Inpatients Length of Stay (2019) x f x2 ≈ 4.97 n2 = 30 s2 ≈ 1.77
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