Question

45 points I A student wonders if tall women tend to date taller men than do short women. She measures herself, her dormitory roommate, and the women in the adjoining rooms; then she measures the next man each woman dates. The data (heights in inches) are listed below Women (x) 67 65 68 62 72 65 Men (v) 71 67 72 69 68 64 (a) Make a scatterplot of these data. (Do this on paper. Your instructor may ask you to turn this in.) Based on the scatterplot, a。you expect the correlation to be positive or negative? Near + 1 or not? The correlation should be positive. It should be near 1. O The correlation should be negative. It should be near -1. O The correlation should be positive. It should not be near 1 The correlation should be negative. It should not be near 1 (b) Find the corrdlation r between the heights of the men and women. (Round your answer to three decimal places.) 0 438 13

Answer 1

(b)

$\sum x= 399$

$\sum y= 411$

$\sum x^2= 26591$

$\sum y^2= 28195$

$\sum xy= 27342$

$S_{xx} = \sum x^2 - \left ( \sum x \right )^2 / n = 26591 - 399^2 / 6 = 57.5$

$S_{yy} = \sum y^2 - \left ( \sum y \right )^2 / n = 28195 - 411^2 / 6 = 41.5$

$S_{xy} = \sum xy - \left ( \sum x \sum y \right ) / n = 27342 - (399*411) / 6 = 10.5$

Correlation r is,

$r = S_{xy} / \sqrt{S_{xx}S_{yy}} = 10.5 / \sqrt{57.5 * 41.5}$

= 0.215