A random number generator should 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 u = 0.5 and = 1/12. Suppose that a command to generate 100 random numbers gives outcomes with mean = 0.42. If the population o remains fixed, suppose that we want to test Ho:=0.5 Ha: + 0.5 a) Is the test statistic statistically significant at the a-0.05 level? b) Is the test statistic statistically significant at the a=0.01 level? c) Calculate the P-value. d) Does the test give good evidence against the null hypothesis? Why or why not? You may use Table C, JMP or a P-value applet TABLE C t distribution critical values Degrees of freedom Confidence level C Z* One-sided P 25 20 15 .10 .05 50% 60% 70% 80% 90% 95% 96% 98% 99% 99.5% 99.8% 99.9% 0.674 0.841 1.036 1.282 1.645 1.960 2.054 2.326 2.576 2.807 3.091 3.291 .025 .02 .01 .005 .0025 .001 .0005 Two-sided .50 50 40 .30 .20 .10 .05 .04 .02 .01 005 .002 .001 P