65. Movies A mathematician exploring the relationship between ratings of movies, their year of release, and their length discov- ered a paradox. Rather than list the data set of 100 movies in the original research, we have created a sample of size 10 that captures the properties of the original dataset. In the table below, the rating is a score from 1 to 10, and the length is in minutes. Source: Journal of Statistics Education. On page 45 and 46 of the etext, do question 65 parts a-d. here is the question Year Rating Length Year Rating Length 2001 10 120 2005 8 115 2003 5 85 2006 6 135 2004 3 100 2007 2 105 2004 6 105 2007 UI 125 2005 4 110 2008 6 130 (a) Find the correlation coefficient between the years since 2000 and the length. (b) Find the correlation coefficient between the length and the (d) Discuss the paradoxical result in part (c). Write what each rating. correlation tells you. Try to explain what is happening. You (c) Given that you found a positive correlation between the may want to look at a scatterplot between the year and the year and the length in part (a), and a positive correlation rating, and consider which points on the scatterplot repre- between the length and the rating in part (b), what would sent movies of length no more than 110 minutes, and which you expect about the correlation between the year and the represent movies of length 115 minutes or more. rating? Calculate this correlation. Are you surprised