Page 173- Q 7.5 A researcher has gathered information from a random sample of 178 households. For each variable below, construct confidence intervals to estimate the population mean. Use the 90% level. a. An average of 2.3 people resides in each household. Standard deviation is 0.35. b. There was an average of 2.1 television sets (s _ 0.10) and 0.78 telephones (s _ 0.55) per household. c. The households averaged 6.0 hours of television viewing per day (s _ 3.0). Q 7.8 A random sample of 500 residents of Shinbone, Kansas, shows that exactly 50 of the respondents had been the victims of violent crime over the past year. Estimate the proportion of victims for the population as a whole, using the 90% confi dence level. (HINT: Calculate the sample proportion P s before using Formula 7.3. Remember that proportions are equal to frequency divided by N.) Q 8.12 page 204 A random sample of 113 convicted rapists in a state prison system completed a program designed to change their attitudes toward women, sex, and violence before being released on parole. Fifty-eight eventually became repeat sex offenders. Is this recidivism rate significantly different from the rate for all offenders (57%) in that state? Summarize your conclusions in a sentence or two. (HINT: You must use the information given in the problem to compute a sample proportion. Remember to convert the population percentage to a proportion.) Q 8.16 You are the head of an agency seeking funding for a program to reduce unemployment among teenage males. Nationally, the unemployment rate for this group is 18%. A random sample of 323 teenage males in your area reveals an unemployment rate of 21.7%. Is the difference significant? Can you demonstrate a need for the program? Should you use a one-tailed test in this situation? Why? Explain the result of your test of significance as you would to a funding agency. Q 9.6 on page 224 and 225 Are college students who live in dormitories signifi cantly more involved in campus life than students who commute to campus? The data below report the average number of hours per week students devote to extracurricular activities. Is the difference between these randomly selected samples of commuter and residential students significant? Sample 1 sample 2 (Residential) (Commuter) X— 1 = 12.4 X— 2 = 10.2 s1 = 2.0 s2 = 1.9 N1 = 158 N2 = 173 Q 9.13 page 225 At St. Algebra College, the sociology and psychology departments have been feuding for years about the respective quality of their programs. In an attempt to resolve the dispute, you have gathered data about the graduate school experience of random samples of both groups of majors. The results are presented below the proportion of majors who applied to graduate schools, the proportion of majors accepted into their preferred programs, and the proportion of these who completed their programs. As measured by these data, is there a significant difference in program quality? Proportion of majors who applied to graduate school are as follows. Sociology psychology P s 1 = 0.53 P s 2 = 0.40 N1 = 150 N2 = 175 b. Proportion accepted by program of first choice are as follows sample 1 sample2 sociology psychology P s 1 = 0.75 P s 2 = 0.85 N1 = 80 N2 = 70 c. Proportion completing the programs are as follows: Sample sample2 (Sociology) (Psychology) P s 1 = 0.75 P s 2 = 0.69 N1 = 60 N2 = 60 Q10.5 Are sexually active teenagers any better informed about AIDS and other potential health problems related to sex than teenagers who are sexually inactive? A 15-item test of general knowledge about sex and health was administered to random samples of teens who are sexually inactive, teens who are sexually active but with only a single partner (“going steady”), and teens who are sexually active with more than one partner. Is there any signifi cant difference in the test scores? Inactive Active –one partner Active—More than Partner One Partner 10 11 12 12 11 12 8 6 10 10 5 4 8 15 3 5 10 15 Q 11.9 Is there a relationship between length of marriage and satisfaction with marriage? The necessary information has been collected from a random sample of 100 respondents drawn from a local community. Write a sentence or two explaining your decision Length of marriage in years Satisfaction Lessthan 5, 5- 10, morethan 10 total Low High total 10 20 30 20 20 40 20 10 30 50 50 100 a. Is there a statistically signifi cant relationship between these variables? b. Compute column percentages for the table to determine the pattern of the relationship. Which group is more likely to be highly satisfi ed?