A high chi-square value indicates:

A high chi-square value indicates:

• A. The results are conclusive.
• B. High probability that results are due to chance.
• C. The sample size is invalid.
• D. Low probability that the results are due to chance.

Answer: (C)

A high chi-square value means the observed counts differ a lot from what would be expected if the null hypothesis were true. In a chi-square test, the statistic sums how far off each category is, weighting by the expected counts. A large value indicates those deviations are unlikely to occur by chance, which is why the p-value becomes small and we reject the null. So the correct interpretation is that there is a low probability that the results are due to chance. This doesn’t guarantee that results are absolutely conclusive—significance depends on the p-value and the study context. It also doesn’t imply that the sample size is invalid; a very large sample can yield a large chi-square even from small discrepancies, though the main takeaway is the low likelihood of such an outcome under the null.

A high chi-square value means the observed counts differ a lot from what would be expected if the null hypothesis were true. In a chi-square test, the statistic sums how far off each category is, weighting by the expected counts. A large value indicates those deviations are unlikely to occur by chance, which is why the p-value becomes small and we reject the null. So the correct interpretation is that there is a low probability that the results are due to chance.

This doesn’t guarantee that results are absolutely conclusive—significance depends on the p-value and the study context. It also doesn’t imply that the sample size is invalid; a very large sample can yield a large chi-square even from small discrepancies, though the main takeaway is the low likelihood of such an outcome under the null.