(a) For the accompanying data set, draw a scatter diagram of the data.
x 2 6 6 7 9
y 3 2 6 9 5

(b) by hand compute the correlation coefficient. r = (round to three decimals as needed.)
(c) Fill in the blanks: Because the correlation coefficient is (positive or negative) and the absolute value of the correlation coefficient, , is (greater or not greater) than the critical value for this data set,___, (no, a positive, or a negative) linear relation exists between x and y.

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.

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step-by-step explanation:

the answer is d

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