Statistics problem: A company wants to estimate the mean net weight of its Cheerios cereal boxes.

Question

A sample of 16 such boxes produced the mean net weight of 31.98 ounces, with a sample standard deviation of 0.26 ounces. Construct a 95% confidence interval for the mean net weight of all Cheerios cereal boxes. Assume that the net weights of all such cereal boxes have a normal distribution.

Answer 1

You do not know the population mean, so you must use a t test with df = 16-1 = 15

Your CI will be μ = xbar ± t* s/sqrt(n)

For CI = .95 we want a tail probability of .025 --> t(df=15) = 2.131

31.98 ± 2.131(,26/4)