In a county wide study, two segments of the Washington County (Wisconsin) population were surveyed about social service needs. One group, referred to as “key informants,” was composed of 77 county leaders: elected officials, business people, and community service providers. The second group consisted of 427 low income individuals who use services in Washington County (source: Washington County Needs Assessment Study, uwrf.edu). When asked to identify significant community problems (from a list of 33 possibilities), members of the “key informants” sample identified an average of 12.3 problems, with a standard deviation of 3.32 problems. Members of the low income sample identified an average of 8.4 community problems, with a standard deviation of 2.5 problems.
a. Build a 95% confidence interval estimate of the difference in the average number of community problems that would be listed by the two populations represented by the samples.
b. Suppose sample sizes had been12 for the key informants sample and 15 for the low income sample. Revise the interval you produced in part a to reflect this change.