Question

EXERCISE 5

The Quality Inspector of a bottle company checks a random sample of 7 elements in two different processes that make the same product and checks the liquid in them.

The results are:

PROCESS 1:        50          49.9       50.2       50.1       50          49.8       50.3

PROCESS 2:       50,2       48,95    49,2       49,5       49,7       50          49,8

Do you think that the production of this plant is following a standard process? Test with an alpha-level of 5 per cent.

Answer 1

Alpha in finance generally referred as the excess / reduced return over a benchmark index and expressed as % of it.

Process 1 results are 50, 49.9, 50.2, 50.1, 50, 49.8 & 50.3, whose average return is  50.04

Process 2 results are 50.2, 48.95, 49.2, 49.5, 49.7, 50 & 49.8, whose average return is  49.62

it seems that both processes follows a standard procedure as both processes average converges to 50 for the same product. If we assume the benchmark process results to be 50, which is an ideal process, then the alpha for both processes can be calculated by formula - ( Average values of samples - Benchmark value ) / Benchmark value

Alpha for process 1 -> (50.04 - 50) / 50 => 0.04 / 50 => +0.08%

Alpha for process 2 -> (49.62 - 50 ) / 50 => -0.38 / 50 => -0.76%

Both processes are standard process as their alpha is also under 5%, which is the limit for a standard process give here.