Question

Data: Fuel economy ratings for different cars.

OLD:   16        27        17        33

NEW: 15        24        12        29

Is there a linear correlation between old ratings and new ratings and explain why. Use an α = 0.05 significance level. The critical value of the Pearson Correlation Coefficient r is 0.950 (for n = 4 and α = 0.05).

Answer 1

To check weather there a linear correlation between old ratings and new ratings we need to compute the sample correlation coefficient, for which we do the following tabulation as:

and the correlation coefficient is calculated as:

Now the sum of squares is calculated as:

Thus the correlation coefficient is calculated as:

Now to check the significance of linear correkation the absolute correalation value must be greater than the absolute critical score of correlation coefficient.

as given The critical value of the Pearson Correlation Coefficient r is 0.950 (for n = 4 and α = 0.05).

Conclusion:

Since the sample correlation is greater than critical score of correlation coefficient hence there is significant correlation between the variables.