Final Answer:
To determine whether there is an association between cola preference and age, a chi-square test for independence needs to be conducted using the given data at the 0.005 significance level.
Step-by-step explanation:
To assess the relationship between cola preference and age, a chi-square test for independence is appropriate. This statistical test examines whether two categorical variables (in this case, cola preference and age groups) are independent or associated in the population.
The observed frequencies from the taste test need to be compared with the expected frequencies if there were no relationship between cola preference and age. The chi-square test calculates a test statistic based on the differences between observed and expected frequencies, considering the degrees of freedom and significance level chosen (in this case, 0.005).
The critical value obtained from the chi-square distribution table will help determine if the calculated chi-square statistic exceeds the critical value. If the calculated chi-square statistic is greater than the critical value, it implies that there is a significant association between cola preference and age. This suggests that cola preference is not independent of age and that there might be a relationship between the two variables in the population.
Consequently, conducting a chi-square test for independence with the provided data will enable us to determine whether there is sufficient evidence at the 0.005 significance level to conclude an association between cola preference and age among the sampled population.