The article "Effects of Bottle Closure Type on Consumer Perception of Wine Quality" (Amer. J. of Enology and Viticulture, 2007: 182-191) reported that in a sample of 106 wine consumers, 22 (20.8%) thought that screw tops were an acceptable substitute for natural corks. Suppose a particular winery decided to use screw tops for one of its wines unless there was strong evidence to suggest that fewer than 25% of wine consumers found this acceptable.
a. Using a significance level of .10, what would you recommend to the winery?
b. For the hypotheses tested in (a), describe in context what the type I and II errors would be, and say which type of error might have been committed.