1. The Professional Golf Association (PGA) measured the putting accuracy of professional golfers playing on the PGA Tour and the best amateur golfers playing in the World Amateur Championship. A sample of 1800 6-foot putts by amateur golfers found 1044 made putts. A sample of 1700 6-foot putts by professional golfers found 1088 made puts.
a. Estimate the proportion of made 6-foot putts by professional golfers. Estimate the proportion of made 6-foot putts by amateur golfers. Which group had a better putting accuracy?
b. What is the point estimate of the difference between the proportions of the two populations? What does this estimate tell you about the percentage of putts made by the two groups of golfers?
c. What is the 97% confidence interval for the difference between the two population proportions? Interpret his confidence interval in terms of the percentage of putts made by the two groups of golfers.
2. A May 1993 New York Times/CBS News poll found that of 500 adults who were planning a vacation in the next six months, 85 were expecting to travel by airplane. A similar survey question in a 2003 New York Times/CBS News poll sampled 700 adults who were planning a vacation during the next six months and found that 189 were expecting to travel by airplane.
a. State the hypotheses that can be used to determine whether a significant change occurred in the population proportion planning to travel by airplane over the 10-year period.
b. What is the sample proportion expecting to travel by airplane in 2003? In 1993?
c. Use α = .06 and test for a significant difference. What is your conclusion?
d. Discuss reasons that might provide an explanation for this conclusion.