Question 7.P.2: A time study analyst wants to estimate the number of observa......
A time study analyst wants to estimate the number of observations that will be needed to achieve a specified maximum error, with a confidence of 95.5 percent. A preliminary study yielded a mean of 5.2 minutes and a standard deviation of 1.1 minutes. Determine the total number of observations needed for these two cases:
a. A maximum error of ± 6 percent of the sample mean.
b. A maximum error of .40 minute.
a. \begin{array}{l}{{x=5.2\,\mathrm{minutes}\qquad\qquad\qquad\qquad{z}=2.00\text{ for 95.5, from p. 307}}}\\ {{s=1.1\,\mathrm{minutes}\qquad\qquad\qquad\qquad a=.06\qquad\qquad\qquad}}\end{array}\\n\,=\,\left({\frac{z s}{a x}}\right)^{2}\ =\,\left({\frac{2.00(1.1)}{.06(5.2)}}\right)^{2}\ =\,49.72;\,{\mathrm{round~to~50~observations}}
b. e\,=\, .40
n\;=\;\left(\frac{z s}{e}\right)^{2}\;=\;\left(\frac{2.00(1.1)}{.40}\right)^{2}\;=\;30.25;\;\mathrm{round~to~31~observations}