At the annual meeting of the Golf Equipment Manufacturer’s Association, a speaker made the claim that at least 30% of all golf clubs being used by nonprofessional United States Golf Association (USGA) members are “knock-offs.” These knock-offs are clubs that look very much like the more expensive originals, such as Big Bertha drivers, but are actually nonauthorized copies that are sold at a very reduced rate. This claim prompted the association to conduct a study to see if the problem was as big as the speaker said. A random sample of 400 golfers was selected from the USGA membership ranks. The players were called and asked to indicate the brand of clubs that they used and several other questions. Out of the 400 golfers, data were collected from 294 of them. Based on the response to club brand, a determination was made whether the club was “original” or a “copy.” The data are in a file called Golf Survey.
a. Based on the sample data, what conclusion should be reached if the hypothesis is tested at a significance level of 0.05? Show the decision rule.
b. Determine whether a Type I or Type II error for this hypothesis test would be more severe. Given your determination, would you advocate raising or lowering the significance level for this test? Explain your reasoning.
c. Confirm that the sample proportion’s distribution can be approximated by a normal distribution.
d. Based on the sample data, what should the USGA conclude about the use of knock-off clubs by the high-handicap golfers? Is the official’s statement justified?