Stats question cant gent right!! Sample Size, population proportion.....true proportion?

1. A line supervisor wants to estimate the proportion of defective parts that are being manufactured by her company to within 2.5%. A sample of 300 components showed that 20 were defective. How large a sample is needed to estimate the true proportion of defective parts with 99% confidence?





I did:


phat = 20/300 = 0.066


C.I = 99% = 2.574


SD = sqrt np(1-p) = 0.06 (0.93) = 0.237





Sample Size = n = (2.574 x 0.237 / 0.025)^2


= 594.57





What am I doing wrong??????Stats question cant gent right!! Sample Size, population proportion.....true proportion?
n = [ 2.574 SD / error ]^2


error = 0.025


SD = sqrt [ p(1-p)] = sqrt [ (0.067)(0.933) ] =0.25





n = [ 2.574 (0.25) / 0.025 ]^2 = 25.74^2 = 662.54 = 663

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