The heights (in inches) and pulse rates (in beats per minute) for a sample of 99
ID: 3375266 • Letter: T
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.
Explanation / Answer
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 rc for a significance level of alpha =0.05,
for a two-tailed test is:
rc = 0.198
Observe that in this case, the null hypothesis is rejected if |r| > rc
|r| > rc =0.198.
|r| = 0.613 > rc = 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.
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