The Hyde Park Neighborhood Association Outreach Committee recently conducted a survey to learn more about the issues and concerns of the residents. In a random sample of 124 residents, 20 indicated...

The Hyde Park Neighborhood Association Outreach Committee recently conducted a survey to learn more about the issues and concerns of the residents. In a random sample of 124 residents, 20 indicated that the main barrier to involvement in community events is scheduling conflicts.30

a. Find a 90% confidence interval for the true proportion of residents who believe the main barrier to involvement in community events is scheduling conflicts.

b. Suppose no prior estimate of p = is known. How large a sample is necessary for the bound on the error of estimation to be 0.04 with confidence level 90%?

When unemployment rises, high school students face more competition from college students and adult workers for summer jobs. In a random sample of 188 high school students looking for summer work, 61 said they were able to find a job.

a. Find a 95% confidence interval for the true proportion of high school students who were able to find a summer job.

 b. In a similar study the previous year, the sample proportion of high school students who were able to find a job was 0.25. Use this estimate to find the sample size necessary for the bound on the error of estimation to be 0.025 with confidence level 95%.