A manufacturer is interested in the output voltage of a powe

A manufacturer is interested in the output voltage of a power supply used in a PC. Output voltage is assumed to be normally distributed with standard deviation 0.25 V. The manufacturer wishes to test H0 : µ = 5 V against Ha : µ 6= 5 V using eight power supplies. If the manufacturer decides to reject H0 if ¯x < 4.85 or if ¯x > 5.15, then

(a) what is the probability of a type I error?

(b) what is the probability that H0 will be rejected if the true mean output voltage is 5.1 V

Solution

Answer to part a)

The rejection region is x < 4.85 and x > 5.15

so the area of these two regions give us the probability of type I error

.

P(x < 4.85) = P( z < (4.85-5)/(0.25/sqrt(8)) = P(z < -1.70) = 0.0445 ~ 0.05

Since it has rejection area under both the tails , the type I error probability = 0.05+0.05 = 0.10 or 10%