Suppose that a random sample of 50 bottles of a particular b

Suppose that a random sample of 50 bottles of a particular brand of cough syrup is selected and
the alchohol content of each bottle is determined. Let denote the average alchohol content for
the population of all bottles of the brand under study. Suppose that the resulting 95% confidence
interval is (7.8,9.4).
a. Would a 90% confidence interval calculated from this same sample have been narrower
or wider than the given interval? Explain your reasoning.
b. Consider the following statement: If the process of selecting a sample size 50 and then
computing the corresponding 95% confidence interval is repeated 100 times, 95 of the
resulting intervals will include . Is this statement correct? Why or why not?

Solution

A 95% CI means that the interval will contain the population mean with 95% confidence.