458 CHAPTER 8 Hypothesis Testing with Two Samples 18. A real estate agent claims that there is no difference between the mean household incomes of two neighborhoods. The mean income of 12 randomly selected households from the first neighborhood is $52,750 with a standard deviation of $2900. In the second neighborhood, 10 randomly selected households have a mean income of $51,200 with a standard deviation of $2225. At a = 0.01, can you reject the real estate agent’s claim? Assume the population variances are equal. Section 8.3 In Exercises 19 –22, test the claim about the mean of the differences for a population of paired data at the level of significance a. Assume the samples are random and dependent, and the populations are normally distributed. 19. Claim: md = 0; a = 0.01. Sample statistics: d = 8.5, sd = 10.7, n = 16 20. Claim: md 6 0; a = 0.10. Sample statistics: d = 3.2, sd = 5.68, n = 25 21. Claim: md … 0; a = 0.10. Sample statistics: d = 10.3, sd = 18.19, n = 33 22. Claim: md ≠0; a = 0.05. Sample statistics: d = 17.5, sd = 4.05, n = 37 In Exercises 23 and 24, (a) identify the claim and state H0 and Ha, (b) find the critical value(s) and identify the rejection region(s), (c) calculate d and sd, (d) find the standardized test statistic t, (e) decide whether to reject or fail to reject the null hypothesis, and (f) interpret the decision in the context of the original claim. Assume the samples are random and dependent, and the populations are normally distributed. 23. A sports statistician claims that the numbers of runs scored in a season by NCAA Division 1 baseball teams changed from 2019 to 2021. The table shows the numbers of runs scored by 10 randomly selected NCAA Division 1 baseball teams in the 2019 and 2021 seasons. At a = 0.05, is there enough evidence to support the sports statistician’s claim? (Source: NCAA) Team 1 2 3 4 5 Runs (2019) 578 377 312 287 387 Runs (2021) 454 345 264 260 363 Team 6 7 8 9 10 Runs (2019) 320 447 334 288 228 Runs (2021) 370 304 313 354 150 24. A physical fitness instructor claims that a weight loss supplement will help users lose weight after two weeks. The table shows the weights (in pounds) of 9 adults before using the supplement and two weeks after using the supplement. At a = 0.10, is there enough evidence to support the physical fitness instructor’s claim? User 1 2 3 4 5 6 7 8 9 Weight (before) 228 210 245 272 203 198 256 217 240 Weight (after) 225 208 242 270 205 196 250 220 240
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