Step 1 :Define the null hypothesis as \(H_{0} ; \sigma=0.04\) and the alternative hypothesis as \(H_{4} ; \sigma<0.04\).
Step 2 :Use the chi-square test statistic for a one-sample test of variance, which is given by the formula \(x^{2} = \frac{(n - 1)s^{2}}{\sigma^{2}}\), where n is the sample size, s is the sample standard deviation, and \(\sigma\) is the hypothesized population standard deviation.
Step 3 :Substitute the given values into the formula: n = 26, s = 0.0378, and \(\sigma\) = 0.04.
Step 4 :Calculate the test statistic to get \(x^{2} = \frac{(26 - 1) * 0.0378^{2}}{0.04^{2}}\).
Step 5 :Compute the value to get \(x^{2} = 22.325625000000002\).
Step 6 :Round the test statistic to three decimal places to get \(x^{2} = 22.326\).
Step 7 :\(\boxed{22.326}\) is the final answer.