Question

8. Given the following table of x and y values, test the claim that there is a significant linear correlation. Use a .05 significance level. You do not have to find an equation.

x|    12    10        9      7       8

y| 175    169   182   146   144

Answer 1

Bafore testing the correlation significance we need to find the correlation coefficient, the table calculation is done for correlation coefficient calculation as:

Now the Sum of squares is caluclated as:

Based on the above table calculations the following is calculated as:

Now the Correlation coefficient is calculated as:

Now to test the claim that there is linear correlation the hypotheses are:

Rejection region:

Reject the Ho if P-value is less than 0.05

Test statistic:

The degree of freedom is calculated as df = n-2 = 5-2 = 3.

P-value:

The P-value is compute dusing the excel formula which is =T.DIST.2T(1.766, 3), THUS THE P-value is computed as 0.1756.

Concusion:

Since the P-value is greater than 0.05 hence we failed to reject the null hypothesis and conclude that there is insufficient evidence to support the claim that there is a significant linear correlation.