Null Hypothesis (H0): The observed distribution matches the claimed distribution. | Alternative Hypothesis (Ha): At least one of the proportions in the null hypothesis is incorrect.

Observed Counts: The actual data collected in each category. | Expected Counts: The values we anticipate seeing in each category if the null hypothesis is true.

Large Chi-Square Value: Indicates a big difference between observed and expected counts, suggesting the null hypothesis might be false. | Small Chi-Square Value: Suggests the observed data is close to what's expected under the null hypothesis.

Small p-value: Results are statistically significant, reject the null hypothesis. | Large p-value: Results are not statistically significant, fail to reject the null hypothesis.

Random: Sample must be randomly selected. | Independence: Population must be at least 10 times the sample size (10% rule).

Expected counts are the values we anticipate seeing in each category if the null hypothesis is true.

The chi-square statistic quantifies how much our observed data deviates from our expected counts.

Degrees of freedom (df) is a parameter that determines the shape of the chi-square distribution; calculated as (Number of Categories) - 1.

The chi-square goodness of fit (GOF) test checks if the observed frequencies of a categorical variable match a hypothesized distribution.

The null hypothesis is the assumption we're testing – usually, it states there's no difference or relationship between variables.

Expected Count = (Sample Size) x (Probability under Null Hypothesis)

$\chi^2 = \sum \frac{(Observed - Expected)^2}{Expected}$

df = (Number of Categories) - 1

Expected Count = (Total Sample Size) * (Proportion under Null Hypothesis). E.g., for Harry Potter: 2500 * 0.33 = 825

$\chi^2 = \frac{(180-200)^2}{200} + \frac{(150-150)^2}{150} + \frac{(170-150)^2}{150}$