A random sample of 25 women resulted in systolic blood pressure levels with a mean of 135 and a standard deviation of 6.8. A random sample of 61 men resulted in systolic blood pressure levels with a mean of 132 and a standard deviation of 1.4. Use a 0.025 significance level and the critical value method to test the claim that blood pressure levels for women vary more than blood pressure levels for men. Enter the smallest critical value. (Round your answer to nearest ten-thousandth.) \begin{tabular}{|c|c|} \hline 1. Extract Information: & \\ \hline 2. Original Claim: & 3. \begin{tabular}{r} $\mathrm{H}_{0}:$ \\ $\mathrm{H}_{1}:$ \end{tabular} \\ \hline 4. Distribution (Graphically): & 6. Test Statistic: \\ \hline & 7. Statistical Conclusion: \\ \hline & 8. Final Words: \\ \hline 5. Critical Value(s): & \\ \hline \end{tabular}

Step 1 ：Extract the given information from the problem: The sample size for women is 25 with a mean of 135 and a standard deviation of 6.8. The sample size for men is 61 with a mean of 132 and a standard deviation of 1.4. The significance level is 0.025.

Step 2 ：Identify the original claim: The blood pressure levels for women vary more than blood pressure levels for men.

Step 3 ：Formulate the null hypothesis (H0) and the alternative hypothesis (H1). H0: The variances of blood pressure levels for women and men are equal. H1: The variance of blood pressure levels for women is greater than for men.

Step 4 ：Visualize the distribution graphically: The distribution will be an F-distribution as we are comparing the variances of two populations.

Step 5 ：Calculate the degrees of freedom for the F-distribution: The degrees of freedom are the sample sizes minus 1. So, for women it is 24 (25-1) and for men it is 60 (61-1).

Step 6 ：Find the critical value(s): The critical value is the value of F such that the area to the right of it under the F-distribution is 0.025. Using the F-distribution table or a statistical software, we find the critical value to be approximately 1.8817.

Step 7 ：Draw a statistical conclusion: If the test statistic is greater than the critical value, we reject the null hypothesis and conclude that the variance of blood pressure levels for women is greater than for men. If the test statistic is less than or equal to the critical value, we do not reject the null hypothesis and conclude that we do not have enough evidence to support the claim that the variance of blood pressure levels for women is greater than for men.

Step 8 ：Final Words: The smallest critical value is \(\boxed{1.8817}\).