576 CHAPTER 10 Chi-Square Tests and the F-Distribution Chapter Quiz 10 Take this quiz as you would take a quiz in class. After you are done, check your work against the answers given in the back of the book. In each exercise, (a) identify the claim and state H0 and Ha, (b) find the critical value and identify the rejection region, (c) find the test statistic, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim. In Exercises 1 and 2, use the table, which lists the distribution of educational achievement for people in the United States ages 25 and older. It also lists the results of a random survey for two additional age groups. (Adapted from U.S. Census Bureau) Ages Educational attainment 25 and older 30–34 65–69 None–8th grade 3.5% 10 23 9th–11th grade 5.5% 23 26 High school graduate 27.6% 80 136 Some college, no degree 15.2% 56 77 Associate’s degree 10.6% 34 41 Bachelor’s degree 23.4% 75 78 Master’s degree 10.6% 31 41 Professional/doctoral degree 3.6% 11 18 1. Does the distribution for people in the United States ages 25 and older differ from the distribution for people in the United States ages 30–34? Use a = 0.05. 2. Use the data for 30- to 34-year-olds and 65- to 69-year-olds to test whether age and educational attainment are related. Use a = 0.01. In Exercises 3 and 4, use the data, which list the annual wages (in thousands of dollars) for randomly selected individuals from three metropolitan areas. Assume the wages are normally distributed and that the samples are independent. (Adapted from U.S. Bureau of Economic Analysis) Ithaca, NY: 53.0, 60.3, 34.6, 37.1, 46.6, 46.8, 41.4, 50.6, 50.8, 49.4, 35.0, 36.7, 57.1 Little Rock, AR: 50.7, 43.7, 53.4, 40.0, 45.2, 52.7, 35.2, 60.4, 40.0, 45.9, 45.7, 47.3, 46.5, 44.5, 31.5 Madison, WI: 62.4, 53.9, 67.6, 52.9, 67.7, 50.7, 62.1, 58.9, 61.1, 65.0, 60.4, 59.6, 51.3, 44.8, 66.2 3. At a = 0.01, is there enough evidence to conclude that the variances of the annual wages for Ithaca, NY, and Little Rock, AR, are different? 4. Are the mean annual wages the same for all three cities? Use a = 0.10. Assume that the population variances are equal.
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