Optical fibers are used in telecommunications to transmit light. Suppose current technology allows production of fibers that transmit light about 50 km. Researchers are trying to develop a new type of glass fiber that will increase this distance. In evaluating a new fiber, it is of interest to test H0: µ = 50 versus Ha: µ > 50, with m denoting the mean transmission distance for the new optical fiber.
a. Assuming s = 10 and n = 10, use Appendix Table 5 to approximate b, the probability of a Type II error, for each of the given alternative values of µ when a test with significance level .05 is employed:
i. 52
ii. 55
iii. 60
iv. 70
b. What happens to β in each of the cases in Part (a) if s is actually larger than 10? Explain your reasoning.