8 In order to test the effect of a drug, a researcher monitors the concentration, \(X\), of a certain protein in the blood stream of patients. For patients who are not taking the drug the mean value of \(X\) is 0.185 . A random sample of 150 patients taking the drug was selected and the values of \(X\) were found. The results are summarised below. $$n = 150 \quad \Sigma x = 27.0 \quad \Sigma x ^ { 2 } = 5.01$$ The researcher wishes to test at the \(1 \%\) significance level whether the mean concentration of the protein in the blood stream of patients taking the drug is less than 0.185 .

1. Carry out the test.
2. Given that, in fact, the mean concentration for patients taking the drug is 0.175 , find the probability of a Type II error occurring in the test.