Discuss the below:
Q: The corporate operations manager for the Phillips Oil Company has his staff working on a new service-station layout plan that would potentially alter the ratio of regular unleaded pumps to other gasoline pumps (premium, super premium, etc) that are placed at a station. As part of the staff's analysis, they are interested in estimating the difference in the population proportion of customers who purchase unleaded regular gasoline in eastern states versus western states. They have considerably more experience with the eastern states. The proportion of customers who purchase unleaded regular gasoline in the eastern states is known to be 0.75. They have sampled 900 western-state customers; 643 of the western-state customers purchased regular unleaded.
a. Using a 95% confidence level, determine the estimate for the population proportion of western-state customers who purchase unleaded regular.
b. On the basis of this confidence interval, would you recommend that Phillips Oil uses a different ratio of regular unleaded pumps in the western states than in the eastern states? Support your answer with the confidence interval and the logic that accompanies it.
c. Referring to part a, what is the margin of error for the confidence interval?
d. Discuss the options that exist to reduce the margin of error.