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To perform a chi-square goodness of fit test, first state the null hypothesis and alternative hypothesis. Then, calculate the expected frequencies for each category and the chi-square test statistic. Finally, compare the calculated chi-square value to the critical value and make a decision.

The null hypothesis states that the observed frequencies in each category are equal to the expected frequencies. The alternative hypothesis states that the observed frequencies are not equal to the expected frequencies.

To calculate the expected frequencies, first determine the total number of observations and the expected proportion for each category. Multiply the total number of observations by the expected proportion to get the expected frequency for each category.

The chi-square test statistic is calculated by summing the squared difference between the observed and expected frequencies for each category, divided by the expected frequency for that category. This gives the chi-square value.

To determine the critical value, use a chi-square distribution table with degrees of freedom equal to the number of categories minus one. Compare the calculated chi-square value to the critical value. If the calculated value is greater than the critical value, reject the null hypothesis. If the calculated value is less than or equal to the critical value, fail to reject the null hypothesis.

In summary, to perform a chi-square goodness of fit test, state the null and alternative hypotheses, calculate the expected frequencies, calculate the chi-square test statistic, and compare the calculated value to the critical value.

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