ODD ANSWERS A87 Real Statistics—Real Decisions for Chapter 9 (page 522) 1. (a) The data appear to have a positive linear correlation. As the annual average of the daily maximum sulfur dioxide concentration increases, the annual average of the daily maximum nitrogen dioxide concentration tends to increase. x Annual average of daily maximum sulfur dioxide concentration (in parts per billion) Annual average of daily maximum nitrogen dioxide concentration (in parts per billion) y 10 20 30 40 50 60 70 80 90 40 42 44 46 48 50 52 54 56 58 60 (b) 0.980. There is a strong positive linear correlation. (c) There is enough evidence at the 5% level of significance to conclude that there is a significant linear correlation between annual averages of the daily maximum concentrations of sulfur dioxide and nitrogen dioxide. (d) ny = 0.242x + 39.403 x Annual average of daily maximum sulfur dioxide concentration (in parts per billion) Annual average of daily maximum nitrogen dioxide concentration (in parts per billion) y 10 20 30 40 50 60 70 80 90 40 42 44 46 48 50 52 54 56 58 60 (e) Yes, for x-values that are within the range of the data set. (f) r2 ≈ 0.961. About 96.1% of the variation in nitrogen dioxide concentrations can be explained by the variation in sulfur dioxide concentrations, and about 3.9% of the variation is unexplained. se ≈ 1.106. The standard error of estimate of the annual averages of the daily maximum concentration of nitrogen dioxide for a specififc annual average of the daily maximum concentration of sulfur dioxide is about 1.106 parts per billion. 2. 43.742 6 y 6 48.616 You can be 95% confident that the annual average of the daily maximum nitrogen dioxide concentration will be between 43.742 and 48.616 parts per billion when the annual average of the daily maximum sulfur dioxide concentration is 28 parts per billion. Chapter 10 Section 10.1 (page 532) 1. A multinomial experiment is a probability experiment consisting of a fixed number of independent trials in which there are more than two possible outcomes for each trial. The probability of each outcome is fixed, and each outcome is classified into categories. 3. 45 5. 57.5 7. (a) H0: The distribution of the ages of moviegoers is 15% ages 2–11, 11% ages 12–17, 11% ages 18–24, 25% ages 25–39, 13% ages 40–49, and 25% ages 50+. (claim) Ha: The distribution of ages differs from the expected distribution. (b) x2 0 = 9.236; Rejection region: x 2 7 9.236 (c) 7.295 (d) Fail to reject H0. (e) There is not enough evidence at the 10% level of significance to reject the claim that the distribution of the ages of moviegoers and the expected distribution are the same. 9. (a) H0: The distribution of the days people order pizza is 14% Sunday, 10% Monday, 11% Tuesday, 12% Wednesday, 13% Thursday, 21% Friday, and 19% Saturday. Ha: The distribution of the days differs from the expected distribution. (claim) (b) x2 0 = 16.812; Rejection region: x 2 7 16.812 (c) 25.086 (d) Reject H0. (e) There is enough evidence at the 1% level of significance to conclude that the distribution of days differs from the expected distribution. 11. (a) H0: The distribution of the number of homicide crimes in California by county is uniform. (claim) Ha: The distribution of homicides by county is not uniform. (b) x2 0 = 30.578; Rejection region: x 2 7 30.578 (c) 214.848 (d) Reject H0. (e) There is enough evidence at the 1% level of significance to reject the claim that the distribution of the number of homicide crimes in California by county is uniform. 13. (a) H0: The distribution of the opinions of Democrat U.S. parents on what path they would prefer their child take after high school is 46% four-year college, 7% two-year college, 19% non-college training program, and 28% all other pathways. Ha: The distribution of opinions differs from the expected distribution. (claim) (b) x2 0 = 7.815; Rejection region: x 2 7 7.815 (c) 63.059 (d) Reject H0. (e) There is enough evidence at the 5% level to support the claim that the distribution of opinions of Democrats and Republicans is different.
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