AP Statistics Flashcards: Carrying Out a Chi-Square Test for Goodness of Fit
Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026
Review key ideas with interactive flashcards. This set includes 16 cards to help you master important concepts.
If your p-value is 0.25 and alpha is 0.10, what is your conclusion?
Because the p-value is greater than alpha, the decision is to fail to reject the null hypothesis (H0).
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If your p-value is 0.25 and alpha is 0.10, what is your conclusion?
Because the p-value is greater than alpha, the decision is to fail to reject the null hypothesis (H0).
How do the results of a chi-square test for goodness of fit contribute to a study?
The results provide statistical reasoning for a research question about a categorical variable's distribution.
What does a larger chi-square test statistic value imply?
A larger chi-square statistic indicates a greater overall difference between the observed and expected counts.
What are the two possible null distributions for the chi-square statistic?
The null distribution for the chi-square statistic can be a randomization distribution or a theoretical chi-square distribution.
What are the key steps, in order, for conducting a chi-square goodness of fit test?
The steps are to calculate the statistic, determine the p-value, interpret the p-value, and justify a claim about the population.
How is a conclusion about the null hypothesis (H0) reached?
The decision to reject or fail to reject H0 is based on comparing the calculated p-value to the significance level, alpha.
Chi-Square Test for Goodness of Fit
A statistical test used to justify a claim about a population's categorical distribution by comparing observed frequencies to expected frequencies.
How is the p-value for a chi-square test for goodness of fit determined?
The p-value for a chi-square test is found by using a chi-square distribution table or technology.
What is the first procedural step mentioned for a chi-square test for goodness of fit?
The first step is to calculate the appropriate chi-square statistic for the test.
What fundamental assumption is made when calculating the p-value?
When calculating the p-value, it is assumed that the null hypothesis (H0) is true.
If your p-value is 0.03 and alpha is 0.05, what is your conclusion?
Because the p-value is less than alpha, the decision is to reject the null hypothesis (H0).
After calculating the p-value, what is the next step in a chi-square test for goodness of fit?
After calculating the p-value, the next step is to interpret the p-value in the context of the problem.
What is the ultimate goal of performing a chi-square test for goodness of fit?
The goal is to justify a claim about the population based on the results of the test.
How are the degrees of freedom (df) calculated for a chi-square test for goodness of fit?
The degrees of freedom are calculated as the number of categories minus 1 (df = number of categories - 1).
What is the formula for the chi-square test statistic?
The chi-square test statistic is calculated as the sum of (Observed - Expected)^2 / Expected for all categories.
Define the p-value in the context of a chi-square test.
The p-value is the probability of obtaining a test statistic as or more extreme than the observed value, assuming the null hypothesis (H0) is true.