Question
A. Ten students obtained the following scores on two short tests, X and Y: (7 points) Students X Y A 7 7 B 8 6
A. Ten students obtained the following scores on two short tests, X and Y: (7 points)
Students | X | Y |
A | 7 | 7 |
B | 8 | 6 |
C | 1 | 12 |
D | 6 | 4 |
E | 5 | 3 |
F | 3 | 10 |
G | 6 | 4 |
H | 5 | 3 |
I | 2 | 6 |
J | 1 | 12 |
1. Construct a scatterplot. (2 points)
2. Describe the relationship you see on the scatterplot in terms of direction and magnitude. (2 points)
3. Calculate the Pearson correlation coefficient. Use two decimal places. (2 points)
4. If the two tests cover the same material, what does the Pearson coefficient measure regarding student performance? (1 point)
B. The following table presents data regarding smoking and lung cancer (United States Department of Health and Human Services, 1982): (8 points)
COUNTRY | Per capita cigarette consumption in the 1930s | Death of men (in millions) from lung cancer in 1950 |
Iceland | 240 | 60 |
Norway | 250 | 90 |
Sweden | 310 | 120 |
Denmark | 370 | 160 |
Australia | 450 | 160 |
Netherlands | 450 | 240 |
Canada | 500 | 150 |
Swiss | 530 | 250 |
Finland | 1110 | 350 |
Uniited Kingdom | 1130 | 460 |
USA | 1280 | 190 |
1. Construct a scatterplot. (2 points)
2. Describe the relationship you see on the scatterplot in terms of direction and magnitude. (2 points)
3. Calculate the Pearson correlation coefficient. Use two decimal places. (2 points)
4. How does your description of direction and magnitude using the scatterplot compare with the result for Pearson's coefficient? (2 points)
C. Use the data from Exercise B to do the following: (5 points) 1. Convert the scores for both variables to an ordinal scale. (2 points) 2. Calculate Spearman's correlation coefficient. (2 points) 3. How does Pearson's correlation coefficient from Exercise B compare with Spearman's correlation coefficient? (1 point)
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