Suppose that a random sample of 50 bottles of a particular brand of cough medicine is selected, and the alcohol content of each bottle is determined. Let m denote the mean alcohol content for the population of all bottles of this brand. Suppose that this sample of 50 results in a 95% confidence interval for μ of (7.8, 9.4).
a. Would a 90% confidence interval have been narrower or wider than the given interval? Explain your answer.
b. Consider the following statement: There is a 95% chance that m is between 7.8 and 9.4. Is this statement correct? Why or why not?
c. Consider the following statement: If the process of selecting a random sample of size 50 and then computing the corresponding 95% confidence interval is repeated 100 times, exactly 95 of the resulting intervals will include μ. Is this statement correct? Why or why not?