Question

Provide an example of where you could use correlation in real life. Explain why a t-test is necessary before you accept this correlation as being real in the population.

Answer 1

(a)

An example of where we could use correlation in real life

We can find the correlation coefficient (r) between hours of study per day (x) and marks in the examination (y).

As a result of the correlation study, we can conclude that there is a strong positive correlation between hours of study per day (x) and marks in the examination. This will be an incentive for any student to devote more time on studies in order to increase his marks in the examination.

(b)

At-test is necessary before we accept this correlation as being real in the population because the reliability of the linear model used in calculation of correlation coefficient (r) between hours of study per day (x) and marks in the examination (y) depends on the number of data points = n in the sample.

Thus, we use t test as follows:
H0: Null Hypothesis: = 0 (The correlation coefficient is not significant)

HA: Alternative Hypothesis: 0 (The correlation coefficient is significant)