Question 7.P.3: Work sampling. An analyst has been asked to prepare an estim......
Work sampling. An analyst has been asked to prepare an estimate of the proportion of time that a turret lathe operator spends adjusting the machine, with a 90 percent confidence level. Based on previous experience, the analyst believes the proportion will be approximately 30 percent.
a. If the analyst uses a sample size of 400 observations, what is the maximum possible error that will be associated with the estimate?
b. What sample size would the analyst need in order to have the maximum error be no more than ± 5 percent?
\hat{p} = .30\qquad z = 1.65 for 90 percent confidence from p. 307
a. e\,=\,z\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\,=\,1.65\sqrt{\frac{.3(.7)}{400}}\,=\,.038
b. n\;=\;\left(\frac{z}{e}\right)^{2}\hat{p}(1\,-\,\hat{p})\,=\,\left(\frac{1.65}{.05}\right)^{2}(.3)(.7)\,=\,228.69,\,\mathrm{or}\,\,229