Math

1.       Five-City Project. The Stanford Five-City Project is a comprehensive community health education study of five moderately sized Northern California towns. Multiple-risk factor intervention strategies were randomly applied to two of the communities. The other three cities served as controls. Outline the design of this study in schematic form.

2.       Campus survey. A researcher conducts a survey to learn about the sexual behavior of college students on a particular campus. A list of the undergraduates at the university is used to select participants. The investigator sends out 500 surveys but only 136 are returned.

a.       Consider how the low response rate could bias the results of this study.

b.      Speculate on potential limitations in the quality of information the researcher will receive on questionnaires that are returned.

3.       Employee counseling. An employer offers its employees a program that will provide up to four free psychological counseling sessions per calendar year. To evaluate satisfaction with this service, the counseling office mails questionnaires to every 10th employee who used the benefit in the prior year. There were 1000 employees who used the benefit. Therefore, 100 surveys were sent out. However, only 25 of the potential respondents completed and returned their questionnaire.

a.       Describe the population for the study.

b.      Describe the sample.

c.       What concern is raised by the fact that only 25 of the 100 questionnaires were completed and returned?

d.      Suppose all 100 questionnaires were completed and returned. Would this then represent an SRS? What type of sample would it be?

4.       Body weight expressed as a percentage of ideal. Body weights of 18 diabetics expressed as a percentage of ideal (defined as body weight ÷ ideal body weight × 100) are shown here. Construct a stem-and-leaf plot of these data and interpret your findings.

107         119         99           114         120         104         88           114         124         116

101         121         152         100         125         114         95           117

5.       Air samples. An environmental study looked at suspended particulate matter in air samples (µg/m3) at two different sites. Data are listed here. Construct side-by-side stemplots to compare the two sites.

Site 1:   68            22           36           32           42           24           28           38

Site 2:   36            38           39           40           36           34           33           32