Review Exercises 573 4. An education researcher claims that the charges for tuition, fees, room, and board at 4-year degree-granting postsecondary institutions are uniformly distributed. To test this claim, you randomly select 800 4-year degree-granting postsecondary institutions and determine the charges for tuition, fees, room, and board at each. The table shows the results. At a = 0.05, test the education researcher’s claim. (Adapted from National Center for Education Statistics) Section 10.2 In Exercises 5 – 8, (a) find the expected frequency for each cell in the contingency table, (b) identify the claim and state H0 and Ha, (c) determine the degrees of freedom, find the critical value, and identify the rejection region, (d) find the chi-square test statistic, (e) decide whether to reject or fail to reject the null hypothesis, and (f) interpret the decision in the context of the original claim. 5. The contingency table shows the results of a random sample of public elementary and secondary school teachers and years of full-time teaching experience. At a = 0.01, can you conclude that the level of instruction is related to the years of full-time teaching experience? (Adapted from U.S. National Center for Education Statistics) Years of full-time teaching experience Level of instruction Less than 3 years 3 – 9 years 10 – 20 years 20 years or more Elementary 99 307 410 235 Secondary 211 670 1001 567 6. The contingency table shows the results of a random sample of individuals by generation and type of vehicle owned. At a = 0.01, can you conclude that generation is related to the type of vehicle owned? Type of vehicle owned Generation Car Truck SUV Van Gen X (ages 41–56) 85 95 44 8 Millennial (ages 25– 40) 110 73 61 4 7. The contingency table shows the results of a random sample of endangered and threatened species by status and vertebrate group. At a = 0.05, test the hypothesis that the variables are independent. (Adapted from U.S. Fish and Wildlife Service) Vertebrate group Status Mammals Birds Reptiles Amphibians Fish Endangered 148 132 39 14 55 Threatened 23 20 24 8 38 Cost Frequency, f $17,000–$19,499 138 $19,500–$21,999 154 $22,000–$24,499 246 $24,500–$26,999 169 $27,000 or more 93
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