In the book, the chi-square distribution is applied to goodness-of-fit test and testing to see if a distribution is normally distributed (Lind et al., 2021). The goodness-of-fit test compared observed frequencies and the distribution to what was expected (Lind et al., 2021). This can be used to help determine if the difference between the expected and actual frequencies are due to change to significantly different. This will also if the information is normally distributed or positively skewed. One example could be gathering information on how many people prefer red, green, blue or yellow hats. Our expectation would be that there is an equal number of hats of each color sold, but the goodness of fit test shows that there is a strong preference for red, blue and green and yellow sold very little. The test helps s determine that the preference is significantly different.

References:

Lind, D. A., Marchal, W. G., & Wathen, S. A. (2021).Statistical Techniques in Business & Economics. McGraw-Hill Education.

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