1. The national AIDS Behavioral Surveys (example 18.1) also interviewed a sample of adults in the cities where AIDS is most common. This sample included 803 heterosexuals who reported having more than one sexual partner in the past year. We can consider this an SRS of size 803 from the population of all heterosexuals in high-risk cities who have multiple partners. These people risk infections with the AIDS virus. Yet 304 of the respondents said they never use condoms. Is this strong evidence that more than one-third of this population never use condoms?
18.1 Risky behavior in the age if AIDS
The National AIDS Behavioral Surveys interviewed a random sample of 2673 adult heterosexuals. Of these, more than 170 had more than one sexual partner in the past year. That's 6.36% of the sample.
2. North Carolina State University looked at the factors that affect the success of college students in a required chemical engineering course. Students must get a C or better in the course in order to continue as chemical engineering majors. There were 65 students from urban or suburban backgrounds, and 52 of these students succeeded. Another 55 students were from rural or small-town backgrounds; 30 of these students succeeded in the course.
(a) Is there good evidence that the proportion of students who succeed is different for urban/suburban versus rural/small-town backgrounds? State hypotheses, give the P- value of a test, and state your conclusion.
(b) Give a 90% confidence interval for the size of the difference.
3. A large study of child care used samples from the data tapes of the Current Population Survey over a period of several years. The result is close to an SRS of child-care workers. The Current Population Survey had three classes of child-care workers: private household, non-household, and preschool teacher. Here are data on the number of blacks among women workers in these three classes.
Household 2455 172
Non-household 1191 167
Teachers 659 86
(a) What percent of each class of child-care workers is black?
(b) Make a two-way table of class workers by race (black or other).
(c) Can we safely use the chi-square test? What null and alternative hypotheses does X squared test?
(d) The chi-square statistic for this table is Xsquared (sorry I can't type this on my computer) = 53.194. What are its degrees of freedom? Use table E to approximate the P- value.
(e) What do you conclude from these data?
Calculation of Confidence Interval, Chi square test for National AIDS Behavioral Survey data.