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 90% confidence using the large-sample method. The number of stores that must be sampled is (Round up to the nearest whole number as needed) B. 310 C. 267 D. 612 Click to select and enter your answer(s) and then click Check Answer.

Explanation / Answer

From the given sample we know p = 52/60 = 0.8667

Required margin of error = 0.05
Confidence interval = 90%
z-value for this CI is 1.64

Margin of error = z * sqrt(p*(1-p)/n)

n = (1.64/0.05)^2 * (0.8667*(1-0.8667))

n = 124.293

hence 124 is the sample size required

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