Caffeine (mg) Sleep (hours) 60 8 0 8 220 5.5 100 7 80 6.5 For caffeine intake, the mean is 92 and the standard deviation is 80.75. For sleep, the mean is 7 and the standard deviation is 1.06.  Calculate the linear correlation coefficient r by hand for this set of paired data values using r=(z_x-z_y)/(n-1). Show your work.  Is the value of r statistically significant? Use Pearson's r table to justify your answer.  Does the value for r and the statistical significance indicate a positive linear correlation, a negative linear correlation, or no linear correlation between the variables caffeine intake and hours of sleep? What does this mean in context?

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