Question

A) What is the difference between testing μd andμ1 = μ2? (In your own words.)

B) What does it mean to have a linear correlation and what does it mean to have a non- linear correlation?

C) Describe the error: Given: The linear correlation coefficient between scores on a math test and scores on a test of athletic ability is negative and close to zero. Conclusion: People who score high on the math test tend to score lower on the test of athletic ability.

Answer 1

a)

μd is the mean of the difference, the difference can be between any two datasets.

Whereas μ1 = μ2 is when we are checking that mean of two datasets are equal or not.

b)

A linear correlation means that both the variables have a linear relation(a straight line relationship) between them. When one changes, the other also changes linearly.

A non-linear correlation means the ratio of change is not constant. It means when all the points on the scatter diagram tend to lie near a smooth curve, the correlation is said to be non linear (curvilinear).

c)

When the linear correlation coefficient is close to zero, it means the variables are correlated weakly.

When we say 'People who score high on the math test tend to score lower on the test of athletic ability', the relation between these two is so weak that these scores doesn't get affected by the other scores.

This statement would have been true if the correlation coefficient magnitude was high.