35. The industry standard for the amount of alcohol poured into many types of drinks (e.g., gin for a gin and tonic, whiskey on the rocks) is 1.5 oz. Each individual in a sample of 8 bartenders with at least ve years of experience was asked to pour rum for a rum and coke into a short, wide (tumbler) glass, resulting in the following data:

2.00 1.78 2.16 1.91 1.70 1.67 1.83 1.48

(summary quantities agree with those given in the article Bottoms Up! The In uence of Elongation on Pouring and Consumption Volume, J. Consumer Res., 2003: 455—463).

a. What does a boxplot suggest about the distribution of the amount poured?

b. Carry out a test of hypotheses to decide whether there is strong evidence for concluding that the true average amount poured differs from the industry standard.

c. Does the validity of the test you carried out in (b)

depend on any assumptions about the population distribution? If so, check the plausibility of such assumptions.

d. Suppose you walk into a bar and ask for a rum and coke. If the bartender has the requisite experience, predict the amount of rum you will get in a way that conveys information about precision and reliability.

e. Suppose the actual standard deviation of the amount poured is .20 oz. Determine the probability of a type II error for the test of

(b) when the true average amount poured is actually (1) 1.6,

(2) 1.7, (3) 1.8.