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 = <u><em>population correlation coefficient.</em></u>
So, Null Hypothesis, : ρ = 0 {means that there is a linear correlation}
Alternate Hypothesis, : ρ
0 {means that there is not a linear correlation}
The test statistics that would be used here <u>One-sample t-test statistics</u> for testing population correlation coefficient;
T.S. = ~
where, r = sample correlation coefficient = 0.948
n = sample of head widths of seals = 6
So, <u><em>the test statistics</em></u> = ~
= 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.