In a poll to estimate presidential popularity, each person in a random sample of

Question

In a poll to estimate presidential popularity, each person in a random sample of 1,110 voters was asked to agree with one of the following statements:

A total of 650 respondents selected the first statement, indicating they thought the president was doing a good job.

Construct a 99% confidence interval for the proportion of respondents who feel the president is doing a good job. (Use Student's t Distribution Table.) (Round your answers to 3 decimal places.)

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?

In a poll to estimate presidential popularity, each person in a random sample of 1,110 voters was asked to agree with one of the following statements:

Explanation / Answer

a. Sample proportion p = 650 / 1110 = 0.5856

1 - p = 1 - 0.5856 = 0.4144

z for 99% = 2.576

Let the confidence interval be (a,b)

a = 650/1110 - 2.576 * ((0.5856*0.4144)/1110) = 0.5475

b = 650/1110 + 2.576 * ((0.5856*0.4144)/1110) =0.6237.

b. Since both values are greater than 0.5, the answer is Yes.

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