Suppose you have a chi-squars GOF test to test null hypothesis that the age distribution of drivers stopped in 2003 for traffic violations is the same as the age distr. in 2002. You compute chi-square= 14.7. At the 5% significance level, what is an appropriate conclusion?
A p-value is less than .05
B p is greater than .05
C Because the conditions for a chi-square GOF test aren't satisfied, you cant' draw an appropriate conclusion.
What does it mean for your p-value if you have a big or small chi-square?
To determine the appropriate conclusion for the chi-square goodness-of-fit (GOF) test, we need to compare the computed chi-square value (14.7) with the critical chi-square value at a given significance level (5%).
First, let's discuss the meaning of the p-value in this context. The p-value is the probability of obtaining a test statistic (in this case, the chi-square value) as extreme as the computed value, assuming that the null hypothesis is true. In simpler terms, it measures the strength of evidence against the null hypothesis.
Now, if the computed chi-square value is large, it indicates a greater discrepancy between the observed and expected values, suggesting a higher likelihood that the two distributions (age distribution of drivers in 2003 and 2002) are different. Conversely, a small chi-square value suggests a smaller discrepancy and a higher likelihood that the distributions are similar.
In this case, we want to assess the appropriateness of the conclusion based on the p-value. Since the p-value is not given directly, we need to compare it with the significance level of 5% (0.05).
If the p-value is less than 0.05, it means that the probability of obtaining the observed discrepancy (or a more extreme one) under the assumption of the null hypothesis is less than 5%. This suggests that the evidence against the null is strong, and we reject the null hypothesis in favor of the alternative hypothesis. Therefore, the appropriate conclusion, in this case, would be option A: "A p-value is less than 0.05."
If the p-value is greater than 0.05, it means that the observed discrepancy is reasonably likely to occur by random chance alone, assuming the null hypothesis is true. In such cases, we fail to reject the null hypothesis. The appropriate conclusion would then be option B: "B p is greater than 0.05."
Option C: "Because the conditions for a chi-square GOF test aren't satisfied, you can't draw an appropriate conclusion," doesn't apply here since you have computed a chi-square value.
To make a conclusive decision, you would need the actual p-value or the critical chi-square value for a specific degree of freedom. Based on the given options, we can assume that the appropriate conclusion is likely to either be A or B.