An initial public offering (IPO) of a company's stock is considered "under-priced" if there is a large percentage difference between its issuing price and its closing price after one day of trading. A Canadian study based on a sample of 399 IPOs, over 25 years, showed that approximately 8% of those stocks were underpriced when they were issued ("The Mixed Results of Canadian IPOs," Canadian Investment Review, Vol. 10, 12-01-1997, pp. 22-26). Suppose that a study of 430 U.S. IPOs had shown that 66 of those issues were underpriced.
a. Use the 0.05 level of significance to test the claim that fewer Canadian IPOs have been underpriced than U.S. IPOs.
b. "Day traders" like underpriced IPOs, because if bought early and sold late on their day of issuance, the trades make a profit. Do the results from (a) support a claim that day traders who knew which IPOs were under-priced could have made more money by investing in U.S. IPOs? What additional information, if any, is needed to answer the question?
c. Construct a 95% confidence interval for the difference in proportions of underpriced IPOs for Canadian and U.S. stocks.