Question

A state meat inspector in Iowa has been given the assignment to estimating the mean net weight of packages of ground chuck labeled "5 pounds." He found that the weight cannot be exactly 5 pounds. A sample of 36 packages reveals that the mean weight is 5.01 pounds. From history data, the population standard deviation is 0.03 pounds.

a. What is the estimated population mean?

b. Determine a 95 percent confidence interval for the population mean.

c. Is it reasonable to say the population mean of the 5 pounds pack is 5.00 pound?

Answer 1

(a) Best estimate of the population mean = 5.01 pounds

(b)

n = 36     

x-bar = 5.01     

s = 0.006     

% = 95     

Standard Error, SE = σ/√n =    0.006 /√36 = 0.001

z- score = 1.959963985     

Width of the confidence interval = z * SE =     1.95996398454005 * 0.001 = 0.001959964

Lower Limit of the confidence interval = x-bar - width =      5.01 - 0.00195996398454005 = 5.008040036

Upper Limit of the confidence interval = x-bar + width =      5.01 + 0.00195996398454005 = 5.011959964

The 95% confidence interval is [5.008 pounds, 5.012 pounds]

(c) No, it is not because 5 lies outside the above confidence interval.