A machine cuts plastic into sheets that are 45feet (540inches) long. Assume that the population of lengths is normally distributed. Complete parts (a) and (b).
(A) The company wants to estimate the mean length the machine is cutting the plastic within 0.5inch. Determine the minimum sample size required to construct a 95% confidence interval for the population mean. Assume the population standard deviation is 1.00inch. n = __
(B) Repeat part (a ) using an error tolerance of 0.25inch. n = __
Which error tolerance requires a larger sample size? Explain.
A. The tolerance E=0.5 inch requires a larger sample size. As error size increases, a larger sample must be taken to ensure the desired accuracy.
B. The tolerance E=0.5 inch requires a larger sample size. As error size decreases, a larger sample must be taken to ensure the desired accuracy.
C.The tolerance E=0.25 inch requires a larger sample size. As error size decreases, a larger sample must be taken to ensure the desired accuracy. D.The tolerance E=0.25 inch requires a larger sample size. As error size increases, a larger sample must be taken to ensure the desired accuracy.