Question

There is a new ultrasound machine that will be marketed to hospitals. The company that makes them claims that it detects more Type Q tumors in early stages than the old technology. A hospital would like to test this claim by using one new machine and one old machine, and recording the proportion of (known) tumors detected with each machine.

- Discuss the merits of a large or small test size, from the hospital’s point of view, based on a comparison of the consequences of the Type I Errors (believing that the new machine is better, but in fact the new machine is the same as the old machine) and Type II Errors (believing that the the old machine is better, but actually the new machine is better).

- Would the CEO of the company building the new machine prefer a lower or higher test size? Explain.

Answer 1

a)

The merits of small test size is that it takes less time, consumes less money, can be easily executed whereas the demerits of it are that it is not highly accurate, it can mislead you also sometimes.

For a large test size, we consumes more time, it takes more money, it also takes more effort to execute it whereas it is the more accurate way, it doesn't mislead us in many cases.

The chances of Type 1 Error and Type 2 error are more in small test size.

b)

The CEO would like to go for a large test size, it can give more accurate result, and it is more reliable.

The chances of Type 1 and Type 2 errors are also less in a large test size.