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 \(\boxed{-3.895}\).