Why is a bivariate normal distribution needed for testing the Product Moment Correlation Coefficient?

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From this information, the question then asked to state an assumption needed to be able to carry out a significance test on the value r, the Pearson Product Moment Correlation Coefficient.

The answer says that the data must have a bivariate normal distribution, or that the points should form an approximate ellipse on a scatter diagram.

Could someone explain this answer, it is not clear to me why those conditions must hold to carry out a significance test.