Final answer:
The critical values for a chi-square distribution with 15 degrees of freedom and a cumulative probability of 0.05 are approximately 7.26 and 24.996.
Step-by-step explanation:
To determine the critical values for the confidence interval for the population variance, we need to find the degrees of freedom (df) and the appropriate critical value. For the given sample size (n = 16) and significance level (α = 0.1), the degrees of freedom are calculated as df = n - 1 = 16 - 1 = 15.
To find the critical value, we need to refer to the chi-square distribution table with 15 degrees of freedom and a cumulative probability of 0.05 (since it's a two-tailed test at a 90% confidence level). From the table, the critical values for a chi-square distribution with 15 degrees of freedom and a cumulative probability of 0.05 are approximately 7.260 and 24.996. These are the critical values to use in the confidence interval formula for the population variance.