Statistical Hypothesis Testing: Practice Problems and Solutions, Exams of Business Statistics

Download Statistical Hypothesis Testing: Practice Problems and Solutions and more Exams Business Statistics in PDF only on Docsity! Stat 202 Chapter 11 Practice Problems Part II Here are some practice problems from the text, along with brief solutions. I don’t think that the text authors do a good job of wording the questions in some cases (it can be hard to tell what to choose for H0 and H1, so I’m also giving you the basic question in my own wording. Some of these problems also ask for confidence intervals. I’m not interested in that: our focus is on hypothesis tests! Problem 11.47 Problem 11.51 Problem 11.87 Problem 11.59 Problem 11.61 Solutions Problem Hypotheses & interpretation of H1 Decision Rule Test Stat p-value Conclusion 11.47 H0: π1 ≥ π2 , or π1 - π2 ≥ 0 H1: π1 < π2 , or π1 - π2 < 0 H1 says aspirin is more effective than the placebo. Group 1 = aspirin users. Reject H0 if z < -2.33 z = -0.49 0.3121 Fail to reject since -0.49 > -2.33, or since p- value > 0.01. The data doesn’t provide evidence that taking aspirin reduces the heart attack risk. 11.51 H0: π1 = π2 , or π1 - π2 = 0 H1: π1 ≠ π2 , or π1 - π2 ≠ 0 H1 says that the proportion of multiple transactions is different, males vs. females Group 1 = males Reject H0 if z < -1.645 or z > 1.645 z = -1.88 0.0602 Reject H0 since -1.88 < -1.645, or since the p- value < 0.10. We do have evidence that the proportion of customers who make multiple transactions is different, males vs. females. (it’s higher for females!) 11.87 H0: π1 ≤ π2 , or π1 - π2 ≤ 0 H1: π1 > π2 , or π1 - π2 > 0 H1 says that the proportion is higher for college group Group 1 = college Reject H0 if z > 2.33. z = 3.09 0.0010 Reject H0 since 3.09 > 2.33, or since 0.001 < 0.01. We conclude that the proportion who use computers IS higher for the college group. Note that this must be an old study. Just about everybody uses computers today!