A statistics teacher wants to know if the proportion of students at his school that are born in certain months is different from the proportion born in other months. He uses school records to determine the birth month of all the students at the school and calculates a chi-square statistic to test the null hypothesis that the proportion born in each month matches the proportion of days of the year that are in each month. Why is this not an appropriate use of a chi-square goodness-of-fit test?

This not an appropriate use of a chi-square goodness-of-fit test because the Statistics teacher ab-initio wished to calculate  the proportion of students at his school that are born in certain months and how significantly different it is from the proportion born in other months. The test of the null hypothesis conducted by the teacher will not going to provide a significant difference as encapsulated in Chi-Square-goodness-of-fit test  as a non-parametric test.

Explanation:

Find vivid explanations from the definition and functions of Chi-Square goodness of fit test is a non-parametric test;

Chi-Square goodness of fit test is a non-parametric test that is used to find out how the observed value of a given phenomena is significantly different from the expected value. ... Then the numbers of points that fall into the interval are compared, with the expected numbers of points in each interval. It further goes to say that Chi-Square goodness of fit test as a non-parametric test is also used to find out how the observed value of a given phenomena is significantly different from the expected value. Then the numbers of points that fall into the interval are compared, with the expected numbers of points in each interval.

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