A poll found that people from the north now have relatively warm feelings toward

Question

A poll found that people from the north now have relatively warm feelings toward people from the south. A poll, conducted by telephone among a random sample of 528 adults, found that 412 of those sampled consider the two regions friends. The margin of error for the poll was plus or minus 3.5 percentage points (for a 0.95 confidence level). Use this information to obtain a 95% confidence interval for the percentage of all northerners who consider the two regions friends. The 95% confidence interval is from % to %.

Explanation / Answer

given

N=528

n=412

P=n/N =412/528 =0.78

since

95% confidence interval is given by

P +/- margin of error

margin of error =0.035

hence

confidence itnerval

0.78 +/- 0.035

hence interval (0.745,0.815)

confidence interval of %

(74.5% ,81.5%)

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