588 CHAPTER 11 Goodness-of-Fit and Contingency Tables 10. Loaded Die The author drilled a hole in a die and filled it with a lead weight, then proceeded to roll it 200 times. Here are the observed frequencies for the outcomes of 1, 2, 3, 4, 5, and 6, respectively: 27, 31, 42, 40, 28, and 32. Use a 0.05 significance level to test the claim that the outcomes are not equally likely. Does it appear that the loaded die behaves differently than a fair die? 11. Mendelian Genetics Experiments are conducted with hybrids of two types of peas. If the offspring follow Mendel’s theory of inheritance, the seeds that are produced are yellowsmooth, green-smooth, yellow-wrinkled, and green-wrinkled, and they should occur in the ratio of 9:3:3:1, respectively. An experiment is designed to test Mendel’s theory, with the result that the offspring seeds consist of 307 that are yellow-smooth, 77 that are green-smooth, 98 that are yellow-wrinkled, and 18 that are green-wrinkled. Use a 0.05 significance level to test the claim that the results contradict Mendel’s theory. 12. Do World War II Bomb Hits Fit a Poisson Distribution? In analyzing hits by V-1 buzz bombs in World War II, South London was subdivided into regions, each with an area of 0.25 km2. Shown below is a table of actual frequencies of hits and the frequencies expected with the Poisson distribution. (The Poisson distribution is described in Section 5-3.) Use the values listed and a 0.05 significance level to test the claim that the actual frequencies fit a Poisson distribution. Does the result prove that the data conform to the Poisson distribution? Number of Bomb Hits 0 1 2 3 4 or more Actual Number of Regions 229 211 93 35 8 Expected Number of Regions (from Poisson Distribution) 227.5 211.4 97.9 30.5 8.7 13. Kentucky Derby The table below lists the frequency of wins for different post positions through the 144th running of the Kentucky Derby horse race. A post position of 1 is closest to the inside rail, so the horse in that position has the shortest distance to run. (Because the number of horses varies from year to year, only the first 10 post positions are included.) Use a 0.05 significance level to test the claim that the likelihood of winning is the same for the different post positions. Based on the result, should bettors consider the post position of a horse racing in the Kentucky Derby? Post Position 1 2 3 4 5 6 7 8 9 10 Wins 1914111516 7 9 12 5 11 14. Super Bowl Betting Pools Super Bowl parties often have a betting pool based on the last digits of scores at the end of each quarter. The table below lists the last digits of scores for all quarters of the Super Bowls up to the time of this writing. Using a 0.05 significance level, test the claim that the last digits occur with the same frequency. What do the results suggest about a betting strategy? Last Digit 0 1 2 3 4 5 6 7 8 9 Frequency 113 25 12 68 46 10 34 80 16 20 15. World Series Games The table below lists the numbers of games played in 110 Major League Baseball (MLB) World Series. This table also includes the expected proportions for the numbers of games in a World Series, assuming that in each series, both teams have about the same chance of winning. Use a 0.05 significance level to test the claim that the actual numbers of games fit the distribution indicated by the expected proportions. Games Played 4 5 6 7 World Series Contests 21 26 24 39 Expected Proportion 2>16 4>16 5>16 5>16
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