A beverage company uses a machine to fill oneliter bottles w

A beverage company uses a machine to fill one-liter bottles with water (see figure). Assume that the population of volumes is normally distributed. (a) The company wants to estimate the mean volume of water the machine is putting in the bottles within 1 milliliter. Determine the minimum sample size required to construct a 90% confidence interval for the population mean. Assume the population standard deviation is 5 milliliters. (b) Repeat part (a) using an error tolerance of 2 milliliters. Which error tolerance requires a larger sample size? Explain. (a) The minimum sample size required for an error tolerance of 1 milliliter is bottles. (b) The minimum sample size required for an error tolerance of 2 milliliters is bottles. Which error tolerance requires a larger sample size? Explain. The error tolerance of requires a larger sample size. As the error size decreases, a sample must be taken to obtain sufficient information from the population to ensure the desired accuracy.

Solution

a)
Compute Sample Size
n = (Z a/2 * S.D / ME ) ^2
Z/2 at 0.1% LOS is = 1.64 ( From Standard Normal Table )
Standard Deviation ( S.D) = 5
ME =1
n = ( 1.64*5/1) ^2
= (8.2/1 ) ^2
= 67.24 ~ 68      
b)
Compute Sample Size
n = (Z a/2 * S.D / ME ) ^2
Z/2 at 0.1% LOS is = 1.64 ( From Standard Normal Table )
Standard Deviation ( S.D) = 5
ME =2
n = ( 1.64*5/2) ^2
= (8.2/2 ) ^2
= 16.81 ~ 17      
The error tolerance of one requires a larger sample size
as the error size decreases a larger sample size must taken