In a hypothesis test using chi-square, if the null hypothesis is true, the sample value of the sample chi-square test statistic will be exactly zero.

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The sample value of the chi-square test statistic can be greater than zero even if the null hypothesis is true, due to sampling variability. It measures the discrepancy between observed and expected frequencies under the null hypothesis, not the absence of any discrepancy.

In a Hypothesis Test Using Chi-Square, If the Null Hypothesis