You are in charge of incoming quality for a chemical plant a

You are in charge of incoming quality for a chemical plant and perform an analysis of every incoming material shipment. For one particular raw material, your specification calls for a sulfur level of less than 50 ppm. Typically your sulfur content tests have a standard deviation of 15 ppm (i.e. assume sigma is 15 ppm and use the normal distribution).   Design a protocol for quality testing that meets the following requirements:

The level of the test (alpha) is .05

The power of the test for detecting a concentration of 60 ppm is at least 0.90

What you need to determine is:

a) how many samples do you need to test, and

b) what is the rejection region? (in other words, at what concentration would you reject the shipment?)

I have found using a computer program that 20 samples are needed but I am not sure how to set up to find the rejection region.

Solution

a)

Power and Sample Size

1-Sample t Test

Testing mean = null (versus < null)

Calculating power for mean = null + difference

? = 0.05 Assumed standard deviation = 15

            Sample Target

Difference    Size   Power Actual Power

       -10      21     0.9      0.903945

The required sample size = 21

b)

the rejection region t with 20 Df at 0.05 level( lower side) = -1.725

if the calculated t < -1.725, reject the null hypothesis

concentration = 50 -1.725*15 =24.125

or observed concentration   < 24.125 then reject