Chapter Test 461 Chapter Test 8 Take this test as you would take a test in class. For each exercise, perform the steps below. (a) Identify the claim and state H0 and Ha. (b) Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed, and whether to use a z-test or a t-test. Explain your reasoning. (c) Find the critical value(s) and identify the rejection region(s). (d) Find the appropriate standardized test statistic. (e) Decide whether to reject or fail to reject the null hypothesis. (f) Interpret the decision in the context of the original claim. 1. In a survey of 5000 students taking the SAT, 350 were undecided on an intended college major. In another survey of 12,000 students taken 10 years before, 360 were undecided on an intended college major. At a = 0.10, can you reject the claim that the proportion of students taking the SAT who are undecided on an intended college major has not changed? (Adapted from College Board) 2. A real estate agency says that the mean home sales price in Olathe, Kansas, is greater than in Rolla, Missouri. The mean home sales price for 39 homes in Olathe is $392,453. Assume the population standard deviation is $224,902. The mean home sales price for 38 homes in Rolla is $285,787. Assume the population standard deviation is $330,578. At a = 0.05, is there enough evidence to support the agency’s claim? (Adapted from Realtor.com) 3. A physical therapist suggests that soft tissue massage therapy helps to reduce the lengths of time patients suffer from headaches. The table shows the numbers of hours per day 18 patients suffered from headaches before and after 6 weeks of receiving treatment. At a = 0.05, is there enough evidence to support the therapist’s claim? Assume the populations are normally distributed. (Adapted from Annals of Musculoskeletal Medicine) Patient 1 2 3 4 5 6 7 8 9 Hours (before) 5.2 5.1 4.9 1.6 6.1 2.3 4.6 5.2 3.1 Hours (after) 3.5 3.3 3.7 2.3 2.7 2.4 2.1 2.5 2.8 Patient 10 11 12 13 14 15 16 17 18 Hours (before) 4.4 4.2 5.4 3.3 5.2 3.7 2.6 2.7 2.6 Hours (after) 4.1 3.0 2.4 2.4 2.7 2.6 2.4 2.7 2.4 4. A demographics researcher claims that the mean household income in a recent year is different for native-born households and foreign-born households. A sample of 18 native-born households has a mean household income of $69,474 and a standard deviation of $21,249. A sample of 21 foreign-born households has a mean household income of $64,900 and a standard deviation of $17,896. At a = 0.01, can you support the demographics researcher’s claim? Assume the populations are normally distributed and the population variances are not equal. (Adapted from U.S. Census Bureau)
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