Suppose that a random sample of 50 bottles of a particular brand of cough syrup is selected and the alcohol content of each bottle determined. Let µ denote the average alcohol content for the population of all bottles of the brand under study. Assume the alcohol content of this brand of cough medicine is normally distributed. Suppose that the sample of 50 results in a 95% confidence interval for µ of (7.8, 9.4). A. Would a 90% confidence interval computed from the data be narrower or wider than the given interval?
B. Consider the following statement: There is a 95% chance that µ is between 7.8 and 9.4. Is this statement correct - yes or no?
C. Consider the following statement: We can be highly confident that 95% of all bottles of this type of cough syrup have an alcohol content that is between 7.8 and 9.4. Is this statement correct - yes or no?
D. Consider the following statement: If the process of selecting a sample of size 50 and computing the corresponding 95% confidence interval is repeated 100 times, about 95 of the resulting intervals will contain µ. Is this statement correct - yes or no?