4. A laboratory test for a metabolic disorder measures the level of an enzyme in blood. In 15 healthy controls the mean level was 14.4 IU per litre and the standard deviation was 3.3. a. How many healthy controls need to be measured in order to limit the standard error of the mean below 0.3 IU per litre? [2] b. After measuring a large group of healthy controls, the mean was found to be 14.9 IU per litre and standard deviation 3.9. Likewise, in a large group of people with the infection the mean was 22.2 IU per litre with standard deviation was 4.9. The company wants to provide recommended cutoffs. Which cutoff archives 95% sensitivity and at which specificity? Conversely, which cutoff provides 95% specificity and at which sensitivity? [9] c. The company decides not to pursue the test further, explain why. [2]