Download A state meat inspector in Iowa has been given the assignment of

A state meat inspector in Iowa has been given the assignment of estimating the mean net
weight of packages of ground chuck labeled “3 pounds.” Of course, he realizes that the
weights cannot be precisely 3 pounds. A sample of 36 packages reveals the mean weight
to be 3.01 pounds, with a standard deviation of 0.03 pounds.
1. What is the estimated population mean?
2. Determine a 95 percent confidence interval for the population mean.
Solution:
1.
The estimated population mean=sample mean = 3.01
2.
95 percent confidence interval for the population mean;
P (Xbar – Zα/2 s/√n < µ < Xbar + Zα/2 s/√n)
n = 36
s = 0.03
Xbar = 3.01
Putting all the given values in the above equation to get 95% Confidence interval,
P (Xbar – Zα/2 s/√n < µ < Xbar + Zα/2 s/√n)
P (3.01 – 1.96 * 0.03/√36 < µ < 3.01 + 1.96 * 0.03/√36) = 0.95
P (3.01 - 0.0098 < µ < 3.01 + 0.0098) = 0.95
P (3.0002 < µ < 3.0198) = 0.95
NOTE:
The 95% confidence interval for the population mean is
P (3.0002 < µ < 3.0198) = 0.95
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