Problem: The headline of a January 31, 2005 USA Today article read, "'January Barometer' predicts a pretty lousy year." Referring to the stock market (and in particular the S&P 500), the article goes on to say that the month of January was "turning out to be a loser and chances are 2005 will be, too." To support the claim, the article presented the S&P 500 performance data for the past 10 years as shown below. Besides the year, the columns are the S&P 500 returns for the month of January and for the entire year. Year January Full Year 1995 2.40% 34.10% 1996 3.30% 20.30% 1997 6.10% 31.00% 1998 1.00% 26.70% 1999 4.10% 19.50% 2000 -5.10% -10.10% 2001 3.50% -13.00% 2002 -1.60% -23.40% 2003 -2.70% 26.40% 2004 1.70% 9.00% 2005 -3.30% As you can see, increases (shown in green) in January are typically associated with increases for the full year, while decreases (shown in red) in January are typically coupled with decreases for the full year. There is, however, a possibility that the association that is seen in the data is due to random chance. What could we do to see if the asserted relationship between January returns and the Full