10.64 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: m 5 50 versus Ha: m . 50, with m denoting the mean transmission distance for the new optical fiber.

a. Assuming s 5 10 and n 5 10, use Appendix Table 5 to approximate

b, the probability of a Type II error, for each of the given alternative values of m when a test with significance level .05 is employed:

i. 52 ii. 55 iii. 60 iv. 70

b. What happens to b in each of the cases in Part (a)

if s is actually larger than 10? Explain your reasoning.