Final answer
The critical value (cv) for a right-tailed chi-square test with 15 degrees of freedom and a significance level (α) of 0.05 is approximately 24.9969.
Step-by-step explanation:
The critical value (cv) is used in hypothesis testing to determine whether to reject the null hypothesis. In a chi-square test, it helps establish the threshold beyond which the test statistic is significant at a specific significance level (α).
For a right-tailed chi-square test with a significance level of 0.05 and 15 degrees of freedom, we refer to chi-square distribution tables or statistical software to find the critical value. Using statistical tables or software, we locate the value that corresponds to the given degrees of freedom and the desired significance level. In this case, with 15 degrees of freedom and a right-tailed test at α = 0.05, the critical value is approximately 24.9969.
The degrees of freedom (df) are calculated as the number of categories or groups minus 1. The significance level (α) is the predetermined threshold for determining the statistical significance of the test.
Having a critical value allows us to compare it to the calculated chi-square test statistic. If the test statistic exceeds the critical value, it suggests that the results are statistically significant at the chosen significance level, leading to the rejection of the null hypothesis in favor of the alternative hypothesis.