A sample sequence of 44 products is selected (in order) from an assembly line. Each product is examined and judged to be either acceptable or defective. A total of 33 of these products were found to be acceptable, and the other 11 were found to be defective. The number of runs was 8 . The runs test is to be used at the 0.05 significance level to test for randomness.
Find the value of the test statistic used in this test, and round it to 3 places after the decimal point (if necessary)
Test statistic:

Step 1 ：Given that the number of acceptable products (n1) is 33, the number of defective products (n2) is 11, the total number of products (n) is 44, and the number of runs (R) is 8.

Step 2 ：The expected number of runs (E(R)) is calculated using the formula \(E(R) = \frac{2n_1n_2}{n} + 1\). Substituting the given values, we get \(E(R) = 17.5\).

Step 3 ：The standard deviation of the number of runs (SD(R)) is calculated using the formula \(SD(R) = \sqrt{ \frac{2n_1n_2(2n_1n_2 - n)}{n^2(n - 1)} }\). Substituting the given values, we get \(SD(R) = 2.439\).

Step 4 ：The test statistic (Z) for the runs test is calculated using the formula \(Z = \frac{R - E(R)}{SD(R)}\). Substituting the given values, we get \(Z = -3.895\).

Step 5 ：Final Answer: The value of the test statistic used in this test is \(\boxed{-3.895}\).