38. Stocks. A young investor in the stock market is concerned that investing in the stock market is actually gambling, since the chance of the stock market going up on any given day is 50%. She decides to track her favorite stock for 250 days and finds that on 140 days the stock was “up.”

a) Find a 95% confidence interval for the proportion of days the stock is “up.” Don’t forget to check the conditions first.

b) Does your confidence interval provide any evidence that the market is not random? Explain.

c) What is the significance level of this test? Explain.