SECTION 7.1 Introduction to Hypothesis Testing 361 41. Survey A polling organization reports that the number of responses to a survey mailed to 100,000 U.S. residents is not 100,000. 42. High School Graduation Rate A high school claims that its mean graduation rate is more than 97%. Interpreting a Decision In Exercises 43– 48, determine whether the claim represents the null hypothesis or the alternative hypothesis. If a hypothesis test is performed, how should you interpret a decision that (a) rejects the null hypothesis? (b) fails to reject the null hypothesis? 43. Swans A scientist claims that the mean incubation period for swan eggs is less than 40 days. 44. Affording Basic Necessities A report claims that more than 30% of households in a Wisconsin county struggle to afford basic necessities. (Adapted from Peninsula Pulse) 45. Lawn Mowers A researcher claims that the standard deviation of the life of a brand of lawn mower is at most 2.8 years. 46. Gas Mileage An automotive manufacturer claims that the standard deviation for the gas mileage of one of the vehicles it manufactures is 3.9 miles per gallon. 47. Marketing A fitness equipment company claims that its competitor’s home gym does not have a customer satisfaction rate of 99%. 48. Rent A recent study claims that at least 20% of renters are behind on rent payments in New Jersey. (Source: National Equity Atlas) 49. Writing Hypotheses: Medicine A medical research team is investigating the mean cost of a 30-day supply of a heart medication. A pharmaceutical company thinks that the mean cost is less than $60. You want to support this claim. How would you write the null and alternative hypotheses? 50. Writing Hypotheses: Transportation Network Company A transportation network company claims that the mean travel time between two destinations is about 16 minutes. You work for one of the company’s competitors and want to reject this claim. How would you write the null and alternative hypotheses? 51. Writing Hypotheses: Backpack Manufacturer A backpack manufacturer claims that the mean life of its competitor’s backpacks is less than 5 years. You are asked to perform a hypothesis test to test this claim. How would you write the null and alternative hypotheses when (a) you represent the manufacturer and want to support the claim? (b) you represent the competitor and want to reject the claim? 52. Writing Hypotheses: Internet Provider An Internet provider is trying to gain advertising deals and claims that the mean time a customer spends online per day is greater than 28 minutes. You are asked to test this claim. How would you write the null and alternative hypotheses when (a) you represent the Internet provider and want to support the claim? (b) you represent a competing advertiser and want to reject the claim?
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