The desired percentage of SiO2 in a certain type of aluminous cement is 5.5. To test whe...

The desired percentage of SiO2 in a certain type of aluminous cement is 5.5. To test whether the true average percentage is 5.5 for a particular production facility, 16 independently obtained samples are analyzed. Suppose that the percentage of SiO₂ in a sample is normally distributed with σ = .3 and = 5.25.

a. Does this indicate conclusively that the true average percentage differs from 5.5? Carry out the analysis using the sequence of steps suggested in the text.

b. If the true average percentage is μ = 5.6 and a level α = .01 test based on n = 16 is used, what is the probability of detecting this departure from H₀?

c. What value of n is required to satisfy α = .01 and β(5.6) = 01?