Question

The Pearson’s coefficient of correlation (r) between a patient’s systolic and diastolic heart rate values was calculated as 0.47 based on eight pairs of measurements. Given that t0.05, 6d.f. = 2.447, determine whether a significant linear correlation exists between the two variables. Explain clearly how you arrive at your conclusion.

Answer 1

The Pearson’s coefficient of correlation (r) between a patient’s systolic and diastolic heart rate values was calculated as 0.47

1. The hypotheses are

Null hypothesis H0: ρ = 0 There is not a significant linear correlation exists between a patient’s systolic and diastolic heart rate.

Alternative Hypothesis HA: ρ ≠ 0 There is a significant linear correlation between a patient’s systolic and diastolic heart rate.

coefficient of correlation r = 0.47, Number of observations (n) = 8

2. Test statistics

t = r n-2 / 1-r2

t = 0.47 * √(8-2) / √(1-(0.47)^2) = 1.3043

Test statistics t = 1.3043

This test statistics follows t distribution with n-2 df. The test is two sided.

3. We have given that two tailed t critical value at α = 0.05, n-2 = 6

tα/2 = t0.025,6 = 2.447

4. If |t|> 2.447 then we reject H0.

Since |t| = 1.3043 < 2.447 so we do not reject H0.

There is not a sufficient evidence to support the claim that there is a significant linear correlation exists between the two variables at 0.05 level of significance.