Final answer:
The value of the chi-square statistic for a distribution with 5 degrees of freedom at the 0.005 level is approximately 15.086, derived from the chi-squared distribution, making answer A) χ²(0.005) = 15.086 correct.
Step-by-step explanation:
The question asks for the value of the chi-square statistic for a chi-square distribution with v = 5 degrees of freedom at the 0.005 level. This is a question related to the chi-squared distribution which is used in hypothesis testing in statistics. To find the value of χ²(0.005), one would generally use a chi-square distribution table or computational tools because these values are determined by the shape of the chi-square distribution which is skewed to the right and varies depending on the degrees of freedom.
Based on the table provided, for 5 degrees of freedom (δf = 5), the chi-square statistic at the p-value of 0.01 is approximately 15.09. Since 0.005 is less than 0.01, the chi-square value for χ²(0.005) would be larger than 15.09. Therefore, the correct answer is A) χ²(0.005) = 15.086, as it is the only option greater than 15.09. Remember that for more precise values, a statistical software or an updated chi-square distribution table should be consulted.