Question

The heights​ (in inches) and pulse rates​ (in beats per​ minute) for a sample of 1111 women were measured. Using technology with the paired​ height/pulse data, the linear correlation coefficient is found to be 0.7200.720. 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=0.050.05.

Answer 1

There is evidence to support the claim that there is a linear correlation between the heights and pulse rates of​ women

Explanation:

given that the heights​ (in inches) and pulse rates​ (in beats per​ minute) for a sample of 11 women were measured.

correlation coefficient r = 0.7200

`H_0 : r=0\\H_a: r \\eq 0`

(two tailed test at 5% significance level)

r difference = 0.7200

Std error of r =
`\sqrt{(1-r^2)/(n-2) } \\=\sqrt{(0.4816)/(9) } \\=0.2313`

Test statistic t = r difference/std error = 3.1128

df =9

p value=0.012458

since p <alpha, we reject H0

There is evidence to support the claim that there is a linear correlation between the heights and pulse rates of​ women