Final answer:
To determine which p-value column to use when comparing a Chi-Square (χ²) value, one must consider the significance level (α) set prior to the test. The correct answer is 0.05.
Step-by-step explanation:
To determine which p-value column to use when comparing the calculated Chi-Square (χ²) value, it is essential to first define the significance level (α) of the test. The significance level is the probability of rejecting the null hypothesis when it is actually true, and is set by the researcher before conducting the test.
In the context of a Chi-Square test, the p-value expresses the probability that the observed differences between the expected and observed frequencies are due to chance. The closer the p-value is to zero, the less likely it is that the observed differences are due to chance, which suggests a significant result.
The choice between p-value columns typically depends on the desired level of confidence or risk one is willing to accept for incorrect conclusions. For most scientific studies, a p-value threshold (α) of 0.05 is commonly used, which corresponds to a 95% confidence level. If the calculated χ² is greater than the critical value at this threshold, then there is sufficient evidence to reject the null hypothesis.
If, however, one wishes to be more conservative and decrease the risk of a Type I error (falsely rejecting a true null hypothesis), a smaller α such as 0.01 would be selected, corresponding to a higher confidence level of 99%. Conversely, if the research context allows for a higher risk of Type I error, a larger α such as 0.10 or 0.20 could be chosen, indicating lower confidence levels of 90% and 80% respectively.