Question

Filaments made at Gloglobe factory are supposed to contain 2.75 mg of chromelite. Because of randomness in the manufacturing process, the amount of chromelite in the filament is actually a random variable. If a filament has more than 2.77 mg or less than 2.73 mg of chromelite, it must be thrown out. Suppose the machines at the factory make filaments with a chromelite distribution which is normally distributed with mean µ = 2.75 mg and standard deviation σ = 0.02 mg of chromelite. Then about 32% of the filaments must be discarded. The factory boss is considering buying a new machine that is known to make filaments of the same mean µ = 2.75 mg, but might have a smaller variance. The boss is interested in testing H0 : σ = 0.02 versus Ha : σ < 0.02. The machines are expensive, so he doesn’t want to make a Type I Error; he sets α = 0.01.

(a) Suppose he gets a random sample of size n = 20 filaments from the new machine. Construct a test statistic and a decision rule.

(b) Suppose the new machine makes filaments with a standard deviation of 0.01 mg of chromelite. What is the power for the test?

(c) Repeat (a) and (b) for a sample size of n = 50.

Answer 1