An article in the Chicago Tribune† reported that in a poll of residents of the C

Question

An article in the Chicago Tribune† reported that in a poll of residents of the Chicago suburbs, 43% felt that their financial situation had improved during the past year. The following statement is from the article: "The findings of this Tribune poll are based on interviews with 930 randomly selected suburban residents. The sample included suburban Cook County plus DuPage, Kane, Lake, McHenry, and Will Counties. In a sample of this size, one can say with 95% certainty that results will differ by no more than 3% from results obtained if all residents had been included in the poll."

Comment on this statement. Give a statistical argument to justify the claim that the estimate of 43% is within 3% of the true proportion of residents who feel that their financial situation has improved. (Round your answers to three decimal places.)

The bound on error for a 95% confidence interval with the given sample proportion of _______ and given sample size of _______ is _______, which is approximately 3%, as stated

Explanation / Answer

Solution:- Given that E = 0.03, p = 0.43 , q = 1-p = 1-0.43 = 0.57 ,95% confidence for Z = 1.96

Fomula : n = (z/E)^2*p*q

n = (1.96/0.03)^2 * 0.43 * 0.57

n = 1046.1957

n = 1046(nearest value)

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