Question

It is suspected that calcium in blood platelets may be related to blood pressure. As part of a study of this relationship, researchers recruited 30 subjects whose blood pressure was normal (i.e., not abnormally elevated). For each subject two measurements were made: pressure (average of systolic and diastolic measurements) and calcium concentration in the blood platelets. The sample size is n = 30, and the sample correlation is r = 0.4. Is there evidence that blood pressure and platelet calcium are linearly related? State the hypothesis and test it at 5% level of significance. What is your conclusion?

Answer 1

Answer:

Step-by-step explanation:

The null and the alternative hypothesis are:

$\mathbf{ H_o: \rho = 0} \\ \\ \mathbf{H_1: \rho \ne 0}$

The test statistics is as follows:

$t = \dfrac{r\sqrt{n-2} }{\sqrt{1-r^2}}$

$t = \dfrac{0.4 \sqrt{30-2} }{\sqrt{1-0.4^2}}$

$t = \dfrac{0.4 \sqrt{28} }{\sqrt{0.84}}$

t = 2.3094

The critical value

$t_{\alpha/df} = t_\ \{0.05/2 \ , \ 30-2 \} } \\ \\ = t_{0.025,28} = \pm 2.048 ( from \ the \ t-tables)$

Decision rule:

To reject $H_o$ if t > $t_{\alpha/df}$.

So since t > $t_{\alpha/df}$. we reject $H_o$ at ∝ = 0.05

Conclusion: There is sufficient evidence to conclude that blood pressure and patient calcium are linearly related.