A machine cuts plastic into sheets that are 40 feet (480 inches) 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 0.5 inch. Determine the minimum sample size required to construct a 90% confidence interval for the population mean. Assume the population standard deviation is 1.00 inch. n[] (Round up to the nearest whole number as needed.) (b) Repeat part (a) using an error tolerance of 0.25 inch. n[] (Round up to the nearest whole number as needed.) Which error tolerance requires a larger sample size? Explain. A. The tolerance E = 0.5 inch requires a larger sample size- As error size increases, a larger sample must be taken to ensure the desired accuracy. 8 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.
Mean = 480 inches
SD = 1 inch
a) 90% confidence interval for withn 0.5 inches from the mean :
For 90% confidence, i.e within 5% < x < 95% ---> z = 1.645
n = z^2 * SD^2 / error^2
Error = (0.5/480) * 100 = 0.1041666666666667
n = z^2 * SD^2 / Error^2
n = 1.645^2 * 1^2 / 0.1041666666666667^2
n = 249.3872639999998403922
n = 249 ---> FIRST ANSWER
-------------------------------------------------------------------------------
Error = (0.25/480) * 100 = 0.0520833333333333%
n = z^2 * SD^2 / Error^2
n = 1.645^2 * 1^2 / 0.0520833333333333^2
n = 997.5490560000012768628
n = 998 ---> SECOND ANSWER
-----------------------------------------------------------------------------------
As can be seen, the case with error tolerance 0.25 inch needs a larger sample size....
Option C ---> THIRD ANSWER
Homework Sourse
