Bluman A.G. Elementary Statistics- A Step By Step Approach

Section 8–6 Additional Topics Regarding Hypothesis Testing 461Corporation agrees to allow you to randomly select 40 of its new Dodge Caravans to test thehighway mileage. Chrysler claims that the vans get 28 mpg on the highway. Your results showa mean of 26.7 and a standard deviation of 4.2. You are not certain if you should create aconfidence interval or run a hypothesis test. You decide to do both at the same time.1. Draw a normal curve, labeling the critical values, critical regions, test statistic, andpopulation mean. List the significance level and the null and alternative hypotheses.2. Draw a confidence interval directly below the normal distribution, labeling the samplemean, error, and boundary values.3. Explain which parts from each approach are the same and which parts are different.4. Draw a picture of a normal curve and confidence interval where the sample andhypothesized means are equal.5. Draw a picture of a normal curve and confidence interval where the lower boundary ofthe confidence interval is equal to the hypothesized mean.6. Draw a picture of a normal curve and confidence interval where the sample mean fallsin the left critical region of the normal curve.See page 470 for the answers.Exercises 8–61. Weekly Earnings for Leisure and Hospitality WorkersThe average weekly earnings in the leisure andhospitality industry group for a recent year was $273. Arandom sample of 40 workers showed weekly averageearnings of $285 with the population standard deviationequal to 58. At the 0.05 level of significance can it beconcluded that the mean differs from $273? Find a 95%confidence interval for the weekly earnings and showthat it supports the results of the hypothesis test.Source: New York Times Almanac.2. One-Way Airfares The average one-way airfare fromPittsburgh to Washington, D.C., is $236. A randomsample of 20 one-way fares during a particular monthhad a mean of $210 with a standard deviation of $43.At a 0.02, is there sufficient evidence to concludea difference from the stated mean? Use the samplestatistics to construct a 98% confidence interval for thetrue mean one-way airfare from Pittsburgh toWashington, D.C., and compare your interval to theresults of the test. Do they support or contradict oneanother?Source: www.fedstats.gov3. IRS Audits The IRS examined approximately 1% ofindividual tax returns for a specific year, and theaverage recommended additional tax per return was$19,150. Based on a random sample of 50 returns, themean additional tax was $17,020. If the populationstandard deviation is $4080, is there sufficient evidenceto conclude that the mean differs from $19,150 ata 0.05? Does a 95% confidence interval support thisresult?Source: New York Times Almanac.4. Canoe Trip Times The average time it takes a person ina one-person canoe to complete a certain river course is47 minutes. Because of rapid currents in the spring, agroup of 10 people traverse the course in an average of42 minutes. The standard deviation, known fromprevious trips, is 7 minutes. Test the claim that thisgroup’s time was different because of the strong currents.Use a 0.10. Find the 90% confidence interval of thetrue mean. Does the confidence interval interpretationagree with the results of the hypothesis test? Explain.Assume that the variable is normally distributed.5. Working at Home Workers with a formal arrangementwith their employer to be paid for time worked at homeworked an average of 19 hours per week. A randomsample of 15 mortgage brokers indicated that theyworked a mean of 21.3 hours per week with a standarddeviation of 6.5 hours. At a 0.05, is there sufficientevidence to conclude a difference? Construct a 95%confidence interval for the true mean number of paidworking hours at home. Compare the results of yourconfidence interval to the conclusion of your hypothesistest and discuss the implications.Source: www.bls.gov6. Newspaper Reading Times A survey taken severalyears ago found that the average time a person spentreading the local daily newspaper was 10.8 minutes.8–63