Suppose that a random sample of 50 bottles of a particular brand of cough syrup is selected
and the alcohol content of each bottle is determined. let denote the average alcohol 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: there is a 95% chance that mu is between 7.8 and 9.4.
is this statement correct? why or why not?

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? why or why not?

d) consider the following statement: if the process of selecting a sample of size 50 and then
computing the corresponding 95% interval is repeated 100 times, 95 of the resulting
intervals will include mu. is this statement correct? why or why not?