1. A Harris poll conducted in August 2014 asked respondents to indicate the prestige they associated with a number of different professions. The top choice was the profession of doctor. The results indicated that 45% of the respondents thought that the profession of doctor had a great deal of prestige, with a margin of error of +/- 4% for a 95% confidence interval.

a. Calculate the lower and upper bounds of the 95% confidence interval.

b. Calculate the confidence interval width.

c. Based on the 95% confidence interval, is it likely that the true population proportion is equal to 50 percent? Explain your answer.

d. Based on the 95% confidence interval, is it likely that the true population proportion is equal to 40 percent? Explain your answer.

2. Results from the same Harris poll indicated that, of the professions included in the poll, the real estate broker/agent profession was considered the least prestigious with 24% of respondents indicating that the profession had no prestige at all, with a margin of error +/- 4% for a 95% confidence interval.

a. Calculate the lower and upper bounds of the 95% confidence interval.

b. Calculate the confidence interval width.

c. Based on the 95% confidence interval, is it likely that the true population proportion is equal to 20 percent? Explain your answer.

d. Based on the 95% confidence interval, is it likely that the true population proportion is equal to 30 percent? Explain your answer.