In a sample of 60 stores of a certain company, 52 violated a scanner accuracy st

Question

In a sample of 60 stores of a certain company, 52 violated a scanner accuracy standard. It has been demonstrated that the conditions for a valid large-sample confidence interval for the true proportion of the stores that violate the standard were not met. Determine the number of stores that must be sampled in order to estimate the true proportion to within 0.05 with 95% confidence using the large-sample method. The number of stores that must be sampled is (Round up to the nearest whole number as needed)

Explanation / Answer

here estimated proportion p=52/60=0.867

for margin of error E=0.05

for 95% CI, z=1.96

hence sample size n=p(1-p)*(Z/E)2 =~178

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