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A goodness-of-fit test is a statistical hypothesis test used to determine how well a sample distribution fits a theoretical distribution, such as the normal distribution. It compares the observed frequencies of data in different categories to the expected frequencies derived from the theoretical model. This test helps assess whether the data follows a specific distribution, which is crucial for validating assumptions in statistical analyses.

Expected frequency refers to the number of occurrences that would be expected in each category of a distribution if the null hypothesis is true. It is calculated by multiplying the total number of observations by the probability of each category. In the context of a goodness-of-fit test, expected frequencies are compared to observed frequencies to evaluate how well the data aligns with the expected distribution.

The normal distribution is a continuous probability distribution characterized by its bell-shaped curve, defined by its mean and standard deviation. It is symmetric around the mean, with most observations clustering around the central peak and probabilities tapering off equally in both directions. Many statistical methods assume normality, making it essential to test whether a dataset follows this distribution, especially in fields like psychology, biology, and social sciences.