408 CHAPTER 7 Hypothesis Testing with One Sample In Exercises 41 and 42, (a) identify the claim and state H0 and Ha, (b) find the critical value(s) and identify the rejection region(s), (c) find the standardized test statistic t, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim. Assume the population is normally distributed. 41. A fitness magazine advertises that the mean monthly cost of joining a health club is $25. You want to test this claim. You find that a random sample of 18 clubs has a mean monthly cost of $26.25 and a standard deviation of $3.23. At a = 0.10, do you have enough evidence to reject the advertisement’s claim? 42. A fitness magazine claims that the mean cost of a yoga session is no more than $14. You want to test this claim. You find that a random sample of 32 yoga sessions has a mean cost of $15.59 and a standard deviation of $2.60. At a = 0.025, do you have enough evidence to reject the magazine’s claim? In Exercises 43 and 44, (a) identify the claim and state H0 and Ha, (b) use technology to find the P-value, (c) decide whether to reject or fail to reject the null hypothesis, and (d) interpret the decision in the context of the original claim. Assume the population is normally distributed. 43. An education publication claims that the mean score for grade 12 students on a science achievement test is more than 145. You want to test this claim. You randomly select 36 grade 12 test scores. The results are listed below. At a = 0.1, can you support the publication’s claim? (Adapted from National Center for Education Statistics) 188 80 175 195 201 143 119 81 118 119 165 222 109 134 200 110 199 181 79 135 124 205 90 120 216 167 198 183 173 187 143 166 147 219 206 97 44. An education researcher claims that the overall average score of 15-year-old students on an international mathematics literacy test is 489. You want to test this claim. You randomly select the average scores of 30 countries. The results are listed below. At a = 0.05, do you have enough evidence to reject the researcher’s claim? (Source: National Center for Education Statistics) 481 507 495 500 499 483 509 515 417 523 526 487 486 519 451 516 454 527 509 495 499 481 508 409 502 491 492 481 496 500 Section 7.4 In Exercises 45– 48, determine whether a normal sampling distribution can be used to approximate the binomial distribution. If it can, test the claim. 45. Claim: p = 0.15; a = 0.05 Sample statistics: np = 0.09, n = 40 46. Claim: p = 0.65; a = 0.03 Sample statistics: np = 0.76, n = 116 47. Claim: p 6 0.70; a = 0.01 Sample statistics: np = 0.50, n = 68 48. Claim: p Ú 0.04; a = 0.10 Sample statistics: np = 0.03, n = 30
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