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.

The correlation coefficient between attendance at physical training (PT) and the score an applicant receives on a physical fitness test (PFT). As a result of this study, I would likely see a strong positive correlation between the attendance at PT and PFT score. This would incentivize applicants to attend PT since it helps improve their PFT score.

A t-test is necessary before we accept this correlation as legitimate in the population because the reliability of the linear model used in calculation of the correlation coefficient between attendance at PT and performance on the PFT depends on the number of data points in the sample used (Lind, Marchal, and Wathen, 2018). The t-test determines how unlikely the correlation coefficient will occur in the population.

Reference:

Lind, D. A., Marchal, W. G., & Wathen, S. A. (2018)Statistical techniques for business and economics. (17th ed.). McGraw-Hill Education.

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