Question

In a poll to estimate presidential popularity, each person in a random sample of 1,190 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 650 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?

Answer 1

(a)

n = 1190    

p = 0.546218487    

% = 95    

Standard Error, SE = √{p(1 - p)/n} =    √(0.546218487394958(1 - 0.546218487394958))/1190 = 0.014432219

z- score = 1.959963985    

Width of the confidence interval = z * SE =     1.95996398454005 * 0.0144322191909479 = 0.02828663

Lower Limit of the confidence interval = P - width =     0.546218487394958 - 0.0282866298312457 = 0.51793186

Upper Limit of the confidence interval = P + width =     0.546218487394958 + 0.0282866298312457 = 0.57450512

The confidence interval is [0.518, 0.575]

(b)

The entire interval above is above 50%, so it is reasonable to conclude that a majority of the population believes the president is doing a good job.

[Please give me a Thumbs Up if you are satisfied with my answer. If you are not, please comment on it, so I can edit the answer. Thanks.]