QUESTION 2 Standard Normal Distribution (22 points) My statistical software has a "random number generator" that is supposed to produce numbers scattered at random between 0 to 1. If this is true, the 'population' average of all random numbers converge to u=0.4. In a sample of 100 random numbers, the sample statistics are as follows: x - 0.62 and of = 0.36. (a) (4 points) Give a 95% and 99% confidence intervals for the true mean. (b) (4 points) Write a short explanation of your findings in (b) for someone who knows no statistics. (c) (3 points) Write down the null and alternative hypotheses and define whether the alternative hypothesis is one-sided or two-sided. Explain what you are testing. (d) (3 points) Compute the one-sample z test statistic. (e) (4 points) Estimate the P-value as accurately as possible using Table C. (f) (4 points) Interpret your answer in part (e). Do you reject or fail to reject the null hypothesis? Use an a=0.05. Is this good evidence that the mean of all randomly-generated numbers is 0.4