Question

A machine that makes dimes is adjusted to make them at diameter 1.9 cm. Production records show that when the machine is properly adjusted, it will make dimes with a mean diameter of 1.9 cm and with a standard deviation of 0.1 cm. During production, an inspector check the diameters of dimes to see if the machine has slipped out of adjustment. A random sample of 64 dimes is selected.

The inspector would like to detect if the true mean diameter happens to reach 1.95 cm at a significance level of a = 0.01. He determines the power of this test to be 0.9228. What is the probability that the inspector will make a Type II Error?

a. 0.01
b. 0.0385
c. 0.05
d. 0.0772
e. 0.9228

Answer 1

0.0772

Explanation:

P(Power) + P(Type II Error) = 1, so P(Type II Error) = 1 – P(Power) = 1 – 0.9228 = 0.0772.