A researcher wishes to know, with 98% confidence, the percentage of women who wear shoes that are too small for their feet. a previous study conducted by the academy of orthopedic surgeons found that 80% of women wear shoes that are too small for their feet. if the researcher wants her estimate to be within 3% of the true proportion, how large a sample is necessary?

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Stacy Gomez

12 April, 04:26

A researcher wishes to know, with 98% confidence, the percentage of women who wear shoes that are too small for their feet. a previous study conducted by the academy of orthopedic surgeons found that 80% of women wear shoes that are too small for their feet. if the researcher wants her estimate to be within 3% of the true proportion, how large a sample is necessary?

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Hayden Fritz · Answer 1

The z-value that corresponds to 98 % confidence is 2.33 from the normal probability table. Variance of proportion p (1-p) = (0.8) (0.2) = 0.16 Standard deviation = 0.4 Sample size n = [ (2.33) (0.4) / 0.03]^2 = 965.1378 = 965