Final answer:
The Chi-Square Goodness-of-Fit Test is used to assess if observed data fit an assumed distribution by comparing observed frequencies to expected frequencies.
Step-by-step explanation:
The name of the goodness of fit test for cross tabulation is the Chi-Square Goodness-of-Fit Test. This statistical test is used to determine whether there is a significant difference between observed frequencies and expected frequencies in one or more categories of a contingency table. It involves calculating a test statistic that follows a chi-square distribution under the null hypothesis, which states that the observed data come from the assumed distribution. The alternative hypothesis suggests that the data do not follow the assumed distribution.
To perform the test, each observed value or cell category must have an expected value of at least five to ensure the validity of the chi-square approximation. The number of degrees of freedom for the test is calculated as the number of categories minus one. Since the goodness-of-fit test is almost always right-tailed, the observed values are compared to the expected values. If the observed and expected values are not close, the test statistic will become very large and appear in the right tail of the chi-square distribution curve.
In practice, when using the goodness-of-fit test, it is essential to round the expected frequencies to two decimal places. For hypothesis testing, the test is suitable for determining if the distribution of data fits a specific theoretical distribution, such as uniform, normal, or other known distributions.