(12 points) Suppose Robbie is the educational director for a group of teen test prep programs in Nevada. He knows that the mean score on Nevada's mathematics exam is 114 points with a standard deviation of 18 points. Robbie thinks the teens in his program score differently than the population mean on Nevada's mathematics exam. To test his claim, he randomly selects 250 of his students and finds the mean test score of the sample to be 117 points. a. What are Robbie's null (H) and alternative (H) hypotheses? A. Ho: H=114 pts and H: B. Ho: 114 pts and H: > C. Ho:x=114 pts and H: x D. Ho: =117 pts and H: 114 pts 114 pts 114 pts 117 pts E. Ho:x=117 pts and H: x > 117 pts b. What is the z-statistic? Give your answer precise to two decimal places. Z c. What is the positive critical value z for a significance level of a= 0.05? Give vour answer precise to at least two decimal places.