Respuesta :
Answer:
We conclude that there is not a linear correlation.
Step-by-step explanation:
We are given that a sample of 6 head widths of seals (in cm) and the corresponding weights of the seals (in kg) was recorded.
Given a linear correlation coefficient of 0.948.
Let ρ = population correlation coefficient.
So, Null Hypothesis, [tex]H_0[/tex] : ρ = 0 {means that there is a linear correlation}
Alternate Hypothesis, [tex]H_A[/tex] : ρ [tex]\neq[/tex] 0 {means that there is not a linear correlation}
The test statistics that would be used here One-sample t-test statistics for testing population correlation coefficient;
T.S. = [tex]\frac{r \times \sqrt{n-2} }{\sqrt{1 -r^{2} } }[/tex] ~ [tex]t_n_-_2[/tex]
where, r = sample correlation coefficient = 0.948
n = sample of head widths of seals = 6
So, the test statistics = [tex]\frac{0.948 \times \sqrt{6-2} }{\sqrt{1 -0.948^{2} } }[/tex] ~ [tex]t_4[/tex]
= 5.957
The value of t-test statistics is 5.957.
Now at 0.01 level of significance, the t table gives a critical value of 4.604 at 4 degrees of freedom for a two-tailed test.
Since our test statistics is more than the critical value of t as 5.957 > 4.604, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.
Therefore, we conclude that there is not a linear correlation.
