Question

The heights (in inches) and pulse rates (in beats per minute) for a sample of 40 women were measured. Using technology with the paired height/pulse data, the linear correlation coefficient is found to be 0.202. Assuming a 0.01 level of significance, find the critical value. Is there sufficient evidence to support the claim that there is a linear correlation between the heights and pulse rates of women?

Answer 1

Answer:

There is not sufficient evidence  to support the claim that there is a linear correlation between the heights and pulse rates of women

Step-by-step explanation:

The correlation coefficient between the variables h(height in inches) and pulse rates (in beats per minute) is 0.202

Sample size n=40

Level of significane alpha = 0.01

Create null and alternate hypothesis as:

H0: r=0

Ha: r not equal 0

(Two tailed test at 1% significance level)

Sample r = 0.202

r difference = 0.202

test statistic t = $\frac{r\sqrt{n-2} }{\sqrt{1-r^2} } \\=\frac{0.202(\sqrt{38} )}{\sqrt{0.9592} } \\=\frac{1.25}{0.9794} \\=1.271$

df =n-2 =38

t critical value for 0.01 and df =38 is 2.704

Since our test statistic lies below 2.704, we accept null hypothesis

There is not sufficient evidence  to support the claim that there is a linear correlation between the heights and pulse rates of women