1. Suppose a factory manufactures electric bulbs. An engineer employed by the factory believes that she has found a new manufacturing technique that will increase the mean life of the bulb, which is currently believed to be at most 450 hours. Suppose the factory management adopts the decision rule on the basis of a sample of bulbs n = 16 to reject the null hypothesis if The standard deviation of bulb life is known to be 40.0 hours and lifetime of a bulb follows a normal distribution.

(a) State the Type I and Type II errors in this context.

(b) Determine , the probability of Type I error.

(c) Determine , the probability of Type II error when in fact and find the power of the test.