Fourteen different second-year medical students took blood pressure measurements of the same patient and the results are listed in the table below. We want to test the claim that there is a linear correlation between systolic (x) and diastolic (y) blood pressures.

Systolic BP (x)Diastolic BP (y)

13882

13091

135100

140100

12080

12590

12080

13080

13080

14498

143105

14085

13070

150100

For parts (1) - (4), refer to the following computer output generated from the sample data:

Pearson Correlation Coefficients, N = 14

Prob > |r| under H0: Rho=0

sbpdbp

sbp1.000000.65788

0.0105

dbp0.657881.00000

0.0105

1.Using the computer output, report the value of the linear correlation coefficient r. For your own practice, calculate the linear correlation coefficient r by hand.

2.Construct a scatterplot of systolic and diastolic blood pressures. Does there appear to be any linear correlation between the two blood pressures? Describe any patterns.

3.Using a 0.05 significance level, test the claim that there is a linear correlation between systolic and diastolic blood pressures. In doing so, write out the hypotheses, the test statistic, the critical value(s) or p-value, and the conclusion.

4.What proportion of the variation in diastolic blood pressures can be explained by the linear association between systolic and diastolic blood pressures?