Respuesta :
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 = [tex]\frac{r\sqrt{n-2} }{\sqrt{1-r^2} } \\=\frac{0.202(\sqrt{38} )}{\sqrt{0.9592} } \\=\frac{1.25}{0.9794} \\=1.271[/tex]
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
The critical value is 0.402; there is not sufficient evidence to support that there is a linear correlation between heights and pulse rates of women.
How to explain the critical value?
For the given data, the following can be deduced:
- Sample size = n = 40
- Correlation coefficient = r = 0.202
- Degrees of freedom = n – 2 = 40 – 2 = 38
- Level of significance = α = 0.01
This test is a two-tailed test. The, required critical value by using the table is given as critical value = 0.402
Here, the correlation coefficient value is less than the critical value, therefore, we reject the null hypothesis.
We then conclude that there is no significant linear correlation between heights and pulse rates of women.
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