A low chi-square value indicates:

A low chi-square value indicates:

• A. Low probability that the results are due to chance.
• B. The results show a perfect fit.
• C. The data are outside the predicted distribution.
• D. High probability that the results are due to chance.

Answer: (D)

A small chi-square value means the observed counts match the expected counts closely. That close match produces a large p-value, indicating there isn’t strong evidence to reject the null hypothesis. In other words, the data could plausibly have occurred by random variation alone. So the results are consistent with chance given the expected distribution. This fits why the other statements aren’t correct: a perfect fit would require zero discrepancy, which is extremely rare in real data; data that are outside the predicted distribution would produce a larger chi-square; and a low chi-square does not imply a low likelihood of chance—quite the opposite, it suggests the observed pattern could easily arise by chance under the null model.

A small chi-square value means the observed counts match the expected counts closely. That close match produces a large p-value, indicating there isn’t strong evidence to reject the null hypothesis. In other words, the data could plausibly have occurred by random variation alone. So the results are consistent with chance given the expected distribution.

This fits why the other statements aren’t correct: a perfect fit would require zero discrepancy, which is extremely rare in real data; data that are outside the predicted distribution would produce a larger chi-square; and a low chi-square does not imply a low likelihood of chance—quite the opposite, it suggests the observed pattern could easily arise by chance under the null model.