Final answer:
The critical value for a chi-square test at the 1% level of significance with 4 degrees of freedom is 13.28, which is not one of the options provided in the question. Therefore, the correct answer is 'none of these.'
Step-by-step explanation:
The question pertains to conducting a chi-square test of independence. The task is to determine if an individual's age and their opinion on the legalization of marijuana are independent. Given a contingency table with observed frequencies and a significance level (alpha) of 1%, we need to calculate the chi-square statistic and compare it with the critical value to determine if the null hypothesis of independence can be rejected. The critical value for a chi-square test at the 1% level of significance with the given degrees of freedom (which is calculated as (rows - 1)*(columns - 1)) can be found in the chi-square distribution table or through statistical software.
To find the correct critical value, we must first determine the degrees of freedom (df). The contingency table has 3 rows and 3 columns, so df = (3-1) * (3-1) = 4. Using a chi-square distribution table at alpha = 1%, the critical value for df = 4 is 13.28. This is not listed in the given options, which means the correct answer to the question must be option a) none of these.
The critical value for a hypothesis test can be determined using the chi-square distribution. In this case, since the significance level is α = 1%, we need to find the chi-square value that corresponds to a cumulative probability of 0.99 (1 - α).
Using the chi-square distribution table with 3 degrees of freedom (4 - 1), we find that the critical value is approximately 12.59. Therefore, the correct answer is option d) 12.59.