Question

The heights (in inches) and pulse rates (in beats per minute) for a sample of

99

women were measured. Using technology with the paired height/pulse data, the linear correlation coefficient is found to be

0.6130.613.

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

alpha?equals=0.050.05.

Click here to view a table of critical values for the correlation coefficient.

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Because

StartAbsoluteValue 0.613 EndAbsoluteValue0.613

is

?

less

greater

than the critical value, there

?

is not

is

sufficient evidence to support the claim that there is a linear correlation between the heights and pulse rates of women for a significance level of

alpha?equals=0.050.05.

Answer 1

The sample size is n=99, so then the number of degrees of freedom is df = n?2 = 99?2 = 97

The corresponding critical correlation value r_c for a significance level of alpha =0.05,

for a two-tailed test is:

r_c = 0.198

Observe that in this case, the null hypothesis is rejected if |r| > r_c

|r| > r_c =0.198.

|r| = 0.613 > r_c = 0.198

The correlation coefficient is greater than critical value

There is sufficient evidence to support the claim that there is a linear correlation between the heights and pulse rates of women for a significance level of alpha=0.05.