Answer:
a) n=5
So then the correlation coefficient would be r =0.430 rounded
b) Null hypothesis:
Alternative hypothesis:
Because the correlation coeffcient is positive and the absolute value of the correlation coefficient 0.430 is not greater than the critical value for this dataset, no linear relation exists between x and y.
And the reason is because we fail to reject the null hypothesis.
Step-by-step explanation:
Part a
We have the following data:
x: 2 6 6 7 9
y: 3 2 6 9 5
The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.
And in order to calculate the correlation coefficient we can use this formula:
For our case we have this:
n=5
So then the correlation coefficient would be r =0.430 rounded
Part b
In order to test the hypothesis if the correlation coefficient it's significant we have the following hypothesis:
Null hypothesis:
Alternative hypothesis:
The statistic to check the hypothesis is given by:
And is distributed with n-2 degreed of freedom. df=n-2=5-2=3
In our case the value for the statistic would be:
The critical value for n =5 is given by the table attached. We can see that the critical value is , and then the final conclusion would be:
Because the correlation coeffcient is positive and the absolute value of the correlation coefficient 0.430 is not greater than the critical value for this dataset, no linear relation exists between x and y
And the reason is because we fail to reject the null hypothesis.
