The following table classifies a stock’s price change as up, down, or no change for both today’s and yesterday’s prices. Price changes were examined for 100 days. A financial theory states that stock prices follow what is called a “random walk.” This means, in part, that the price change today for a stock must be independent of yesterday’s price change. Test the hypothesis that daily stock price changes for this stock are independent. Let a = 0.05.

Price Change Previous Day Price Change Today Up No Change Down Up 14 16 12 No Change 6 8 6 Down 16 14 8