A small British computer-game firm, Eidos Interactive PLC, stunned the U.S.- and Japan-dominated market for computer games when it introduced Lara Croft, an Indiana Jones-like adventuress. The successful product took two years to develop. One problem was whether Lara should have a swinging ponytail, which was decided after taking a poll.
If in a random sample of 200 computer-game enthusiasts, 161 thought she should have a swinging ponytail (a computer programmer's nightmare to design), construct a 95% confidence interval for the proportion in this market.
If the decision to incur the high additional programming cost was to be made if p > 0.90, was the right decision made (when Eidos went ahead with the ponytail)?