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

Explanation:

The null and the alternative hypothesis are:

`\mathbf{ H_o: \rho = 0} \\ \\ \mathbf{H_1: \rho \\e 0}`

The test statistics is as follows:

`t = (r√(n-2) )/(√(1-r^2))`

`t = (0.4 √(30-2) )/(√(1-0.4^2))`

`t = (0.4 √(28) )/(√(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.