Your company is changing its name, and you’ve been asked to study the impact of a name change announcement on the subsequent return generated by the firm’s stock. In a sample of 400 companies that have made such announcements, you discover that over the 28-day period after a name
change announcement, the average company experiences a 17 percent increase in price, with a standard deviation of 8 percent.
a. What is a 90 percent confidence interval for the mean stock price change for companies announcing a name change?
b. The range from 16 percent to 18 percent would constitute what (percentage) confidence interval for the mean change?

c. Do the data suggest that there is at least a 75 percent chance that a company’s stock price will go up after a name change announcement?