MATH 533 Week 5 Homework Problems/Solutions (Summer 2019)
- Question 7.2.11: Several years ago, a government agency reported the default rate (the proportion of borrowers who default on their loans) on a certain type of loan at 0.055. Set up the null and alternative hypotheses to determine if the default rate this year is greater than 0.55.
- Question 7.2.13: A university economist conducted a study of elementary school lunch menus. During the state-mandated testing period, school lunches averaged 877 calories. The economist claimed that after the testing period ended, the average caloric content of the school lunches increased significantly. Set up the null and alternative hypothesis to test the economist’s claim.
- Question 7.3.21: For the α and observed significance level (p-value) pair, indicate whether the null hypothesis would be rejected. Α 0.05, p value = 0.45
- Question 7.3.22: Consider testing H0: µ = 20 against Ha : µ < 20 where µ is the mean number of latex gloves used per week by all hospital employees, based on the summary statistics n = 41, x̄ = 19.3, and s = 11.6. Complete parts a and
- Question 7.3.23: In a test of H0: µ = 20 against Ha : µ > 20, the sample data yielded the test statistic z = 1.87. Find and interpret the p-value for the test.
- Question 7.3.26: Consider a test of H0: µ = 75 performed with the computer. The software reports a two-tailed p-value of 0.1094. make the appropriate conclusion for each of the following situations.
- Question 7.4.38: Researchers investigated the physiological changes that accompany laughter. Ninety subjects (18-34 years old) watched film clips designed to evoke laughter. During the laughing period, the researchers measured the heart rate (beats per minute) of each subject, with the following summary results: x̄ = 73.5, s = 7. It is well known that the mean resting heart rate of adults is 71 beats per minute. Complete parts a through d below.
- Question 7.4.41: The final score of games of a certain sport were compared against the final point spreads established by oddsmakers. The difference between the game outcome and point spread (called a point-spread error) was calculated for 215 games. The sample mean and sample standard deviation of the point-spread errors are x̄ = 1.5, and s = 12.2. Use this information to test the hypothesis that the true mea point-spread error for all games is larger than 0. Conduct the test at α = 0.05 and interpret the result.
- Question 7.5.54: When bonding teeth, orthodontists must maintain a dry field. A new bonding adhesive has been developed to eliminate the necessity of a dry field. However, there is concern that the new bonding adhesive is not as strong as the current standard, a composite adhesive. Tests on a sample of 9 extracted teeth bonded with the new adhesive resulted in a mean breaking strength (after 24 hours) of x̄ = 4.69 Mpa and a standard deviation of s = 0.46 Mpa. Orthodontists want to know if the true mean breaking strength is less than 5.34 Mpa, the mean breaking strength of the composite adhesive.
- Question 7.5.59-T: A recent study investigated tractor skidding distances along a road in a forest. The skidding distances (in meters) were measured at 20 randomly 7 selected road sites. The data are … in the accompanying table. A logger working on the road claims that the mean skidding distance is at least 425 meters. Is there sufficient evidence to refute this claim? Use α = 0.10
- Question 7.6.71: A business journal investigation of the performance and timing of corporate acquisitions discovered that in a random sample of 2,730 firms, 764 announced one or more acquisitions during the year 2000. Does the sample provide sufficient evidence to indicate that the true percentage of all firms that announced one or more acquisitions during the year 2000 is less than 29%? Use α = 0.05 to make your decision.
- Question 7.6.75-T: In a representative sample of 782 coffee growers from Country X, 388 growers were certified to sell to organic coffee markets while 62 growers were transitioning to become organic certified. In Country Y, 61% of coffee growers are organic … Is there evidence to indicate that fewer than 61% of the coffee growers in Country X are either organic certified or transitioning to become organic certified? State your conclusion so that there is only a 10% chance of making a Type | error.
Name: Jennifer Lucas
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