Moore, 6.48: Testing a random number generator: A random number generator is supposed to generatenumbers uniformly distributed between 0 and 1. If this is true, then the population mean shouldbe .5; you generate 100 random numbers and get sX = x = .522 with standard deviation .316. Youinterpret this standard deviation as the population standard deviation.

(a) You want to test that the mean is .5. What is the hypothesis?

(b) Calculate the test statistic.

(c) Do we have evidence that the mean is not .5? Would it matter if we used = .1, .05, or .01?

(d) Suppose you believed that the generator was consistently biased upward. Would your hypothesischange?