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 1,430 voters was asked to agree with one of the following statements:

A total of 525 respondents selected the first statement, indicating they thought the president was doing a good job.

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.)

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 1,430 voters was asked to agree with one of the following statements:

Explanation / Answer

a) Confidence interval for population proportion is
Sample proportion +/- Confidence coefficient*Standard error of p
=> Sample proportion = p^ = x/n = 525/1430 = 0.367

Confidence coefficient is the critical value of z for 95% confidence level = 1.96
Standard error of p = sqrt [p*(1-p)/n]
= sqrt [(0.367*0.633)/1430]

= 0.013

=> Therefore, the required CI = 0.367 +/- 0.013

  lower boundary is 0.367 - 0.013 = 0.354

upper boundary is   0.367 + 0.013 =0.380

The CI is (0.354,0.380)

b)   YES,

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