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 .\\
(i) Carry out the test.\\

(ii) 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.\\

\hfill \mbox{\textit{CAIE S2 2017 Q8}}