Answer to Question #120065 in Statistics and Probability for Benedict

Question

If the Senator decides to purchase and distribute Norvasc (a medicine that reduces blood pressure), based on your results in (i), which age group (youth or old adults) should be given priority? Briefly explain your answer.

Answer 1

$$\def\arraystretch{1.5} \begin{array}{c:c} & X & Y & XY & X^2 & Y^2 \\ \hline & 20 & 80 & 1600 & 400 & 6400 \\ & 25 & 85 & 2125 & 625 & 7225 \\ & 50 & 125 & 6250 & 2500 & 15625 \\ & 30 & 90 & 2700 & 900 & 8100 \\ & 45 & 100 & 4500 & 2025 & 10000 \\ & 60 & 135 & 8100 & 3600 & 18225 \\ & 10 & 80 & 800 & 100 & 6400 \\ & 15 & 70 & 1050 & 225 & 4900 \\ & 35 & 100 & 3500 & 1225 & 10000 \\ & 70 & 140 & 9800 & 4900 & 19600 \\ Sum=& 360 & 1005 & 40425 & 16500 & 106475 \end{array}$$

$$\bar{X}={1\over n}\displaystyle\sum_{i=1}^nX_i={360\over 10}=36$$

$$\bar{Y}={1\over n}\displaystyle\sum_{i=1}^nY_i={1005\over 10}=100.5$$

$$S_{XX}=\displaystyle\sum_{i=1}^nX_i^2-{1\over n}(\displaystyle\sum_{i=1}^nX_i)^2=$$ $$=16500-{1\over 10}(360)^2=3540$$

$$S_{YY}=\displaystyle\sum_{i=1}^nY_i^2-{1\over n}(\displaystyle\sum_{i=1}^nY_i)^2=$$ $$=106475-{1\over 10}(1005)^2=5472.5$$

$$S_{XY}=\displaystyle\sum_{i=1}^nX_iY_i-{1\over n}(\displaystyle\sum_{i=1}^nX_i)(\displaystyle\sum_{i=1}^nY_i)=$$ $$=40425-{1\over 10}(360)(1005)=4245$$

Correlation coefficient

$$r={S_{XY}\over \sqrt{S_{XX}}\sqrt{S_{YY}}}$$

$$r={4245\over \sqrt{3540}\sqrt{5472.5}}\approx0.9645$$

This is a strong positive correlation, which means that high X variable scores go with high Y variable scores (and vice versa).

$$B={S_{XY}\over S_{XX}}={4245\over 3540}\approx1.1992$$

$$A=\bar{Y}-B\bar{X}=100.5-{4245\over 3540}(36)\approx57.3305$$

$$y=57.3305+1.1992x$$

Old adults should be given priority. Older adults suffer from high blood pressure.