In a chi-square goodness-of-fit test, we lose one degree of freedom for each parameter estimated.

Question

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This statement is true. In a chi-square goodness-of-fit test, the expected frequencies for each category or group are calculated based on some hypothesized distribution. These expected frequencies are then compared to the observed frequencies, and the difference between the two is measured using a chi-square statistic. The number of degrees of freedom for the test is equal to the number of categories or groups minus one. However, if any parameters (such as the mean or standard deviation of the hypothesized distribution) are estimated from the data, an additional degree of freedom is lost for each parameter estimated. This is because estimating a parameter from the data reduces the overall amount of variability in the chi-square statistic.

In a Chi-Square Goodness-Of-Fit Test, We Lose One Degree of Freedom