The Chi-square test for goodness of fit is a statistical method used to analyze if observed frequency distributions significantly differ from expected ones. It's applied in scenarios like testing the fairness of a die or assessing the distribution of species in a lake. The test involves calculating a Chi-square statistic and comparing it to a critical value or computing a p-value to validate the hypothesis.
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The Chi-square test is a statistical procedure used to determine if there is a significant difference between an observed frequency distribution and an expected probability distribution
Goodness of fit refers to the evaluation of how well observed data fit with a specified theoretical distribution
The purpose of the Chi-square test for goodness of fit is to test the hypothesis that an observed frequency distribution follows a particular expected distribution
The Chi-square test for goodness of fit assumes the use of a simple random sample, a categorical variable, expected frequencies of at least five in each category, and the independence of observations
Prerequisites for the Chi-square test include a simple random sample, a categorical variable, adequate expected frequencies, and the independence of observations
The Chi-square statistic is calculated using the formula χ² = Σ[(Oi - Ei)² / Ei], where 'Oi' is the observed frequency and 'Ei' is the expected frequency for each category
The Chi-square test is executed by selecting a significance level and comparing the calculated Chi-square statistic to a critical value or p-value
Examples of the Chi-square test for goodness of fit include studying the distribution of fish species in a lake and eye colors among students in a classroom setting
The Chi-square test for goodness of fit is commonly used in various fields of study to evaluate how well observed data fit with a specified theoretical distribution
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When testing if a six-sided die is fair, the expected frequency for each side is ______ of the total rolls.
one-sixth
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Chi-square test purpose
Evaluates if observed distribution significantly differs from expected.
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Chi-square test outcome interpretation
Low probability of observed under H0 leads to its rejection.
