The Mill Valley Brewery distributes beer in bottles labeled as 32oz, and claims their standard deviation to be 0.75oz. The Bureau of Weights and Measures randomly selects 50 of these bottles, measures their contents, and obtains a sample mean of 31.7oz.

a) What is the sampling distribution of xbar, and how do you know that?

b) Assuming the beer is properly filled as labeled, how likely was it to have gotten a mean of 31.8 from their sample?

Using a 0.05 significance level, test the Bureau's claim that the brewery is cheating their consumers. What is... c) ...the null hypothesis?

d) ...the alternative hypothesis?

e) ...the test statistic?

f) ...the critical value?