A ski company in Vail owns two ski shops, one on the east side and one on the west side. Sales data showed that at the eastern location there were 56 pairs of large gloves sold out of 304 total pairs sold. At the western location there were 145 pairs of large gloves sold out of 562 total pairs sold.
(a) Calculate the sample proportion of large gloves for each location.
(b) At α = .05, is there a significant difference in the proportion of large gloves sold?
(c) Can you suggest any reasons why a difference might exist?