The glass transition temperature (Tg) describes the temperature at which a material transitions from rigid to flexible. Plastic pool liners need to have Tg below -20C.

During process validation, a manufacturer measures the following from 8 samples: Tg (C): -15.5, -19.5, -23.0, -12.0, -25.0, -14.0, -17.0, -21.0

a) Check the assumption that the sample data is normally distributed.

b) Test the hypothesis that the process produces pool liners that do not have a Tg > -20C. Use an = 0.05 and make all necessary assumptions.

c) How many samples are needed to be able to show a true mean of -15C can be detected with a power of 0.90 and an = 0.05?