Problems 4 are based on the following table which shows the stock market performance of 40 industries from five sectors of the U S economy as of noon on September 11 2015 Take S to be the set of all 40 industries represented in the table Increased X Decreased Y Financials F Manufacturing M Unchanged Z Totals 4 1 Totals 24 3 8 Information Technology T Health Care H 4 Utilities U 3 10 6 1 3 4 Test the following pairs of events for independence a Z M 3 40 8 065 14 7 b X U c Does the fact that a selected industry is a manufacturing industry make it more or less likely that its stock market performance increased Solution