As a manufacturer of golf equipment, the Spalding Corporation wants to estimate the proportion of golfers who are left-handed. The company intends to use this information in planning for the number of right-handed and left-handed sets of golf clubs to make during future production.
a) Assuming that there is no available information that could be used as an estimate of p how many golfers must be surveyed if we want 99% confidence that the sample proportion has a margin of error of 0.025? Show your work.
b) Assume instead that we have an estimate of p from a previous study that suggests that 15% of golfers are left-handed (based on a USA Today report). Based on this new information, how many golfers must be surveyed if we want 99% confidence that the sample proportion has a margin of error of 0.025? Show your work.
c) Let's now assume that instead of randomly selected golfers, the sample data are obtained by asking TV viewers of the golfing channel to call an "800" phone number to report whether they are left-handed or right-handed. How might the results be affected? Explain.