A machine cuts plastic into sheets that are 35 feet (420 inches) long. Assume th

Question

A machine cuts plastic into sheets that are 35 feet (420 inches) long. Assume that the population of lengths is normally distributed. Complete parts (a) and (b). The company wants to estimate the mean length the machine is cutting the plastic within 0.125 inch. Determine the minimum sample size required to construct a 95% confidence interval for the population mean. Assume the population standard deviation is 0.25 inch. N=? (Round up to the nearest whole number as needed.) (b) Repeat part (a) using an error tolerance of 0.0625 inch. n=? (Round up to the nearest whole number as needed.) Which error tolerance requires a larger sample size? Explain. A. The tolerance E=0.0625 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=0.125 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=0.125 inch requires a larger sample size. As error size increases, a larger sample must be taken to ensure the desired accuracy. D. The tolerance E=0.0625 inch requires a larger sample size. As error size decreases, a larger sample must be taken to ensure the desired accuracy.

Explanation / Answer

a.Here it is given that We=0.125 with sd=0.25 and z value is 1.96 for 95% CI

Hence n=(z*sd/E)^2=(1.96*0.25/0.125)^2=15.334=16

Now for E=0.0625

n=((1.96*0.25)/0.0625)^2=62

Answeris

D. The tolerance E=0.0625 inch requires a larger sample size. As error size decreases, a larger sample must be taken to ensure the desired accuracy.

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