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

Section 9–1 Testing the Difference Between Two Means: Using the z Test 481Based on the following information, can the researchers’claim be supported at the 0.05 level of significance?Retired DisabledSample size 60 60Mean benefit $960.50 $902.89Population standard deviation $98 $101Source: New York Times Almanac.15. Self-Esteem Scores In the study cited in Exercise 11,the researchers collected the data shown here on a selfesteemquestionnaire. At a 0.05, can it be concludedthat there is a difference in the self-esteem scores of thetwo groups? Use the P-value method.LeaversStayersX 1X 2 3.05 2.96s 1 0.75 s 2 0.75n 1 103 n 2 225Source: Paula Rayman and Belle Brett, “Women ScienceMajors: What Makes a Difference in Persistence afterGraduation?” The Journal of Higher Education.16. Ages of College Students The dean of studentswants to see whether there is a significant difference inages of resident students and commuting students. Sheselects a sample of 50 students from each group. The agesare shown here. At a 0.05, decide if there is enoughevidence to reject the claim of no difference in the agesof the two groups. Use the P-value method. Assumes 1 3.68 and s 2 4.7.Resident students22 25 27 23 26 28 26 2425 20 26 24 27 26 18 1918 30 26 18 18 19 32 2319 19 18 29 19 22 18 2226 19 19 21 23 18 20 1822 21 19 21 21 22 18 2019 23Commuter students18 20 19 18 22 25 24 3523 18 23 22 28 25 20 2426 30 22 22 22 21 18 2019 26 35 19 19 18 19 3229 23 21 19 36 27 27 2020 21 18 19 23 20 19 1920 2517. Problem-Solving Ability Two groups of students aregiven a problem-solving test, and the results are compared.Find the 90% confidence interval of the truedifference in means.Mathematics majors Computer science majorsX 1 83.6 X 2 79.2s 1 4.3 s 2 3.8n 1 36 n 2 362.8 m 1 m 2 6.018. Credit Card Debt The average credit card debt for arecent year was $9205. Five years earlier the averagecredit card debt was $6618. Assume sample sizes of 35were used and the population standard deviations ofboth samples were $1928. Is there enough evidence tobelieve that the average credit card debt has increased?Use a 0.05. Give a possible reason as to why or whynot the debt was increased.Source: CardWeb.com19. Literacy Scores Adults aged 16 or older were assessedin three types of literacy in 2003: prose, document, andquantitative. The scores in document literacy were thesame for 19- to 24-year-olds and for 40- to 49-year-olds.A random sample of scores from a later year showed thefollowing statistics.PopulationMean standard SampleAge group score deviation size19–24 280 56.2 4040–49 315 52.1 35Construct a 95% confidence interval for the truedifference in mean scores for these two groups. Whatdoes your interval say about the claim that there is nodifference in mean scores?Source: www.nces.ed.gov20. Battery Voltage Two brands of batteries are tested, andtheir voltage is compared. The data follow. Find the 95%confidence interval of the true difference in the means.Assume that both variables are normally distributed.0.3 m 1 m 2 0.5Brand XBrand YX 1 9.2 voltsX 2 8.8 voltss 1 0.3 volts 2 0.1 voltn 1 27 n 2 30Extending the Concepts21. Exam Scores at Private and Public Schools Aresearcherclaims that students in a private school haveexam scores that are at most 8 points higher than thoseof students in public schools. Random samples of 60 studentsfrom each type of school are selected and given anexam. The results are shown. At a 0.05, test the claim.Private schoolX 1Public schoolX 2 110 104s 1 15 s 2 15n 1 60 n 2 609–11