When the chi-squared test statistic is greater than the critical value, what conclusion can be drawn?

When the chi-squared test statistic is greater than the critical value, what conclusion can be drawn?

• A. There is no significant difference
• B. The null hypothesis cannot be rejected
• C. There is significant evidence to reject the null hypothesis
• D. Accept the alternative hypothesis

Answer: (C)

When the chi-squared test statistic exceeds the critical value, it indicates that the observed data significantly deviates from what would be expected under the null hypothesis. This deviation suggests that the variables are likely associated in some way or that the distribution of the observed data differs from the expected distribution. Consequently, there is significant evidence to reject the null hypothesis, meaning that we have sufficient statistical support to conclude that a relationship or difference exists in the context being studied. This conclusion is foundational in hypothesis testing, where the rejection of the null hypothesis implies that the results are unlikely to have occurred purely by chance under the assumption of that hypothesis.

When the chi-squared test statistic exceeds the critical value, it indicates that the observed data significantly deviates from what would be expected under the null hypothesis. This deviation suggests that the variables are likely associated in some way or that the distribution of the observed data differs from the expected distribution.

Consequently, there is significant evidence to reject the null hypothesis, meaning that we have sufficient statistical support to conclude that a relationship or difference exists in the context being studied. This conclusion is foundational in hypothesis testing, where the rejection of the null hypothesis implies that the results are unlikely to have occurred purely by chance under the assumption of that hypothesis.