Question

In a poll to estimate presidential popularity, each person in a random sample of 990 voters was asked to agree with one of the following statements: 1. The president is doing a good job. 2. The president is doing a poor job. 3. I have no opinion. A total of 700 respondents selected the first statement, indicating they thought the president was doing a good job. a. Construct a 95% confidence interval for the proportion of respondents who feel the president is doing a good job. (Use z Distribution Table.) (Round your answers to 3 decimal places.) Confidence interval for the proportion is up to . b. Based on your interval in part (a), is it reasonable to conclude that a majority of the population believes the president is doing a good job? Yes No

Answer 1

(A) we know the formula for confidence interval

CI =

we have p^ = 700/990 = 0.71 and n = 990

z score for 95% is 1.96 (using z distribution table)

setting the values in the above formula, we get

Confidence interval = = (0.6817, 0.7383)

so, the required 95% confidence interval is (0.6817, 0.7383)

(B) We are 95% confidence that the percent of people who believes that president is doing a good job is between 68.17% to 73.83%

so, it is clear that majority of people believes that the president is doing a good job because the we are 95% confidence that the percent of people who believes that president is doing a good job is between 68.17% to 73.83%

we know that any percent more than 50%, makes it majority.