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Unformatted text preview: n? 7 (Weirs pg 344, 10.60) PROBLEM # 8.19 ­For a simple random sample, n=200 and p=0.34. At the 0.01 level, test H0:!! =0.40 versus H1:!! ≠0.40. PROBLEM # 8.20 ­ For a simple random sample, n=1000 and p=0.47. At the 0.05 level, test H0:!! ≥0.50 versus H1:!! <0.50. 8 PROBLEM # 8.21 A simple random sample of 300 items is selected from a large shipment, and testing reveals that 4% of he sampled items are defective. The supplier claims that no more than 2% of the items in the shipment are defective. Carry out an appropriate hypothesis test and comment on the credibility of the supplier’s claim. PROBLEM # 8.22 It has been claimed that 65% of the homeowners would prefer to hear with electricity instead of gas. A student finds that 60% of the 200 homeowners prefer electric heating to gas. In a two ­tail test at the 0.05 level of significance, can we conclude that the percentage who prefer electric heating may differ from 65%? Determine and interpret the p ­value for the test. 9 PROBLEM # 8.23 For each of the following situations, determine whether a one ­tail test or a two ­tail test would be appropriate. Describe the test, including the null and alternative hypotheses, then explain your reasoning in selecting it. a. A machine that has not been serviced for several months is producing output in which 5% of the items are defective. The machine has just been serviced and quality should now be improved. b. In a speech during her campaign for reelection, a Republican candidate claims that 55% of registered Democrats in her county intend to vote for her. c. Of those who have bought a new car in the part, a dealer has found that 70% experience three or more mechanical problems in the first four months of ownership. Unhappy with this percentage, the dealer has heavily revised the procedure by which pre ­delivery mechanical checks are carried out. PROBLEM # 8.24 What is a p ­value, and how it is relevant to hypothesis testing? 10 PROBLEM # 8.25 The p ­value for a hypothesis test has been reported as 0.03. If the test result is interpreted using the ! =0.05 level of significance as a criterion, will H0 be rejected? Explain. PROBLEM # 8.26 A hypothesis test is carried out using the ! =0.01 level of significance and H0 cannot be rejected. What is the most accurate statement we can make about the p ­value for this test? Understanding the Basics: Suggested Problems from the Book. 8.1 The Null and Alternative Hypotheses and Errors in Hypothesis Testing: 8.2,8.4,8.6,8.8,8.10,8.16 8.2 Type I and Type II Errors and Their Probabilities 8.3 z Tests about a population Mean (! unknown): One ­Sided Alternatives: 8.18,8.20,8.24,8.26,8.28,8.32,8.34 8.4 z Tests about a population Mean (! known): Two ­Sided Alternatives: 8.40,8.42,8.45,8.46, 8.5 t Tests about Population Mean (! unknown): 8.48,8.50,8.52,8.56, 8.6 z Tests about Population Proportion: 8.62,8.64,8.66,8.68, End of Chapter: 8.76,8.78,8.79,8.82,8.83,8.84 This statistical workbook is compiled from the following books: • • • Keller, G. (2012). Statistics for management and economics. Mason: Cengage Learning. Weiers, R. M. (2011). Introduction to Business Statistics. Mason: Cengage Learning. Gonick, L. W. (2005). The Cartoon Guide to Statistics (Vol. 1). HarperCollins. Samie’s Tips! Lesson 8 ­The Exam corner ­ TIPS and TRICKS! Hello, We are now reaching the period of “hypothesis testing”, from now on, all chapters will be about testing a hypothesis using a specific table and knowing whether you should be using the t ­tables, z ­tables, f ­table or X2 table. Understand the 7 steps and you should be okay. See you in class! Samie 11...
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