A post-mix beverage machine is adjusted to release a certain amount of syrup into a chamber where it is mixed with carbonated water. A random sample of 25 beverages was found to have a mean syrup content of ¯x = 1.098 fluid ounces and a standard deviation of s = 0.016 fluid ounces.

(a) Do the data presented in this exercise support the claim that the mean amount of syrup dispensed is not 1.0 fluid ounce? Test this claim using ? = 0.05.
(b) Do the data support the claim that the mean amount of syrup dispensed exceeds 1.0 fluid ounce? Test this claim using ? = 0.05.
(c) Consider the hypothesis test in part (a). If the mean amount of syrup dispensed differs from µ = 1.0 by as much as 0.05, it is important to detect this with a high probability (at least 0.90, say). Using s as an estimate of ?, what can you say about the adequacy of the sample size n = 25 used by the experimenters?
(d) Find a 95% two-sided CI on the mean amount of syrup dispensed.