In a small town, the relationship between robberies and police officers on duty has been collected. x represents the number of police officers on duty and y represents the number of reported thefts. x 10 15 16 1 4 6 18 12 14 7 y 5 2 1 9 7 8 1 5 3 6. at alpha = 0.01 what is the critical value for r ? (values are +/-)

Step-by-step explanation:

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=10

So then the correlation coefficient would be r =-0.9690

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=10-2=8

In our case the value for the statistic would be:

Since then and using the degrees of freedom we see that the critical values that accumulates 0.005 of the area on each tail are:

and

And in our case since our calculated value it's outside of the interval (-3.36;3.36) we can reject the null hypothesis at 1% the significance.

answer:      

step-by-step explanation:

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