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

Section 9–4 Testing the Difference Between Proportions 511interval of the true difference in the proportions. Doesthe confidence interval contain 0? Why would this factbe important to a researcher?Source: Based on statistics from the American Veterinary Medical Association.12. Bullying Bullying is a problem at any age butespecially for students aged 12 to 18. A study showedthat 7.2% of all students in this age bracket reportedbeing bullied at school during the past six months with6th grade having the highest incidence at 13.9% and12th grade the lowest at 2.2%. To see if there is adifference between public and private schools,200 students were randomly selected from each. Atthe 0.05 level of significance, can a difference beconcluded?PrivatePublicSample size 200 200No. bullied 13 16Source: www.nces.ed.gov13. Survey on Inevitability of War A sample of 200teenagers shows that 50 believe that war is inevitable,and a sample of 300 people over age 60 shows that93 believe war is inevitable. Is the proportion ofteenagers who believe war is inevitable different fromthe proportion of people over age 60 who do? Usea 0.01. Find the 99% confidence interval for thedifference of the two proportions.14. Hypertension It has been found that 26% of men20 years and older suffer from hypertension (high bloodpressure) and 31.5% of women are hypertensive. Arandom sample of 150 of each gender was selected fromrecent hospital records, and the following results wereobtained. Can you conclude that a higher percentage ofwomen have high blood pressure? Use a 0.05.MenWomenSource: www.nchs.gov43 patients had high blood pressure52 patients had high blood pressure15. Partisan Support of Salary Increase Bill Findthe 99% confidence interval for the difference in thepopulation proportions for the data of a study inwhich 80% of the 150 Republicans surveyed favoredthe bill for a salary increase and 60% of the200 Democrats surveyed favored the bill for a salaryincrease. 0.077 p 1 p 2 0.32316. Airlines On-Time Arrivals The percentages of ontimearrivals for major U.S. airlines range from 68.6 to91.1. Two regional airlines were surveyed with thefollowing results. At a 0.01 is there a difference inproportions?Airline AAirline BNo. of flights 300 250No. of on-time flights 213 185Source: New York Times Almanac.17. Senior Workers It seems that people are choosing orfinding it necessary to work later in life. Randomsamples of 200 men and 200 women age 65 or olderwere selected, and 80 men and 59 women were found tobe working. At a 0.01, can it be concluded that theproportions are different?Source: Based on www.census.gov18. Smoking Survey National statistics show that 23% ofmen smoke and 18.5% of women do. A random sampleof 180 men indicated that 50 were smokers, and of150 women surveyed, 39 indicated that they smoked.Construct a 98% confidence interval for the truedifference in proportions of male and female smokers.Comment on your interval—does it support the claimthat there is a difference? 0.0961 p 1 p 2 0.1319Source: www.nchs.gov19. College Education The percentages of adults 25 yearsof age and older who have completed 4 or more yearsof college are 23.6% for females and 27.8% for males.A random sample of women and men who were25 years old or older was surveyed with these results.Estimate the true difference in proportions with 95%confidence, and compare your interval with theAlmanac statistics.WomenMenSample size 350 400No. who completed 4 or more years 100 115Source: New York Times Almanac.Extending the Concepts20. If there is a significant difference between p 1 and p 2 andbetween p 2 and p 3 , can you conclude that there is asignificant difference between p 1 and p 3 ?No, p 1 could equal p 3 .9–41