17.18 Testing a Random Number Generator. A random number generator is supposed to produce random numbers that are uniformly distributed on the interval from 0 to 1. If this is true, the numbers generated come from a population with " ! 0.5 and ! ! 0.2887. A command to generate 100 random numbers gives outcomes with mean x ! 0.4365. Assume that the population ! remains fixed. We want to test H0: " ! 0.5 Ha: " ! 0.5

(a) Calculate the value of the z test statistic.

(b) Use Table C: is z statistically significant at the 5% level 1# ! 0.052?

(c) Use Table C: is z statistically significant at the 1% level 1# ! 0.012?

(d) Between which two Normal critical values z* in the bottom row of Table C does z lie? Between what two numbers does the P-value lie? Does the test give good evidence against the null hypothesis?