Question

The heights​ (in inches) and pulse rates​ (in beats per​ minute) for a sample of 90 women were measured. Using technology with the paired​ height/pulse data, the linear correlation coefficient is found to be 0.351. Is there sufficient evidence to support the claim that there is a linear correlation between the heights and pulse rates of​ women? Use a significance level of alphaαequals=0.01

Answer 1

Let denotes the true linear correlation coefficient between the heights and pulse rates of​ women.

To test against

Here

sample correlation coefficient r = 0.351

and sample size n = 90

The test statistic can be written as

which under H₀ follows a t distribution with n-1 df.

We reject H₀ at 1% level of significance if p-value < 0.01

Now,

The value of the test statistic

and p-value =

Since p-value = 0.000694 < 0.05, so we reject H₀ at 1% level of significance and we can conclude that there is enough evidence to support the claim that there is significant linear correlation between the heights and pulse rates of​ women