Which statement about chi-square with a large chi-square value is true?

Which statement about chi-square with a large chi-square value is true?

• A. The probability that results are due to chance is high.
• B. The results show a perfect fit.
• C. The p-value is large.
• D. The probability that results are due to chance is low.

Answer: (D)

Interpreting the chi-square statistic: a large chi-square value means the observed frequencies differ a lot from what the null hypothesis would expect, so such data would be unlikely if the null were true. That translates to a small p-value, indicating that the probability of obtaining these results by chance is low. So the true statement is that the probability results are due to chance is low. The idea of a perfect fit or a large p-value doesn’t fit with a large chi-square, which signals a poor fit and a small p-value, not the opposite.

Interpreting the chi-square statistic: a large chi-square value means the observed frequencies differ a lot from what the null hypothesis would expect, so such data would be unlikely if the null were true. That translates to a small p-value, indicating that the probability of obtaining these results by chance is low. So the true statement is that the probability results are due to chance is low. The idea of a perfect fit or a large p-value doesn’t fit with a large chi-square, which signals a poor fit and a small p-value, not the opposite.