(d) (8 points) The width of the confidence interval of part (b) is approximately 13.04 miles. How many samples would we need to take to obtain a 90% confidence interval of at most the same width? width? How many samples would we need to take to obtain a 99% confidence interval of at most the same (e) (8 points) Suppose the university previously asserted that the true mean distance travelled by students was 325 miles. Describe the null hypothesis (Ho) and alternative hypothesis (Ha) if we believe that the previous claim by the university is not true. (f) (6 points) Construct a rejection region for Mo with a = 0.05. Can we reject the null hypothesis in favor of the alternative hypothesis? Why or why not?1. Does the average Washington State University student drive more or less than 300 miles from Pullman to home? In a sample of 226 students, the sample mean mileage was 285 miles with a sample standard deviation of 50 miles. Plotting the data, we see that the sample is approximately normal. (a) (4 points) Determine if a one-sided or two-sided confidence interval is appropriate for this situation. Explain your reasoning. (b) (10 points) Compute a 95% confidence interval for M. Write your solution in interval notation. Interpret the meaning of the interval in the context of the situation. (c) (4 points) Compared the the confidence interval calculated above, if the confidence level is decreased to 90%, the new confidence interval is - If the confidence level is increased to 99%, the new confidence interval is A. wider, wider B. narrower, narrower C. wider, narrower D. narrower, wider Page 1 of 9Explain. (g) (4 points) Determine the p-value for Mo. Is this p-value consistent with your solution to part (f)? (h) (6 points) Which of the following are TRUE about the significance level a in hypothesis testing? Circle all that apply. A. a = 0.01 requires stronger evidence for rejecting Ho than a = 0.05. B. a is the probability or chance rejecting a true Ho (Type I error). C. We reject Ho if the p-value is more than a. D. a = 0.05 means that 95% of all such hypothesis tests correctly retains Ho. E. All of the above. (i) (5 points (bonus)) If the variance of this situation is unknown, what important theorem tells us that Z = " ~ N(0, 1) for large samples? In general, what is the minimum sample size necessary to apply this theorem? What distribution does the test statistic follow if the sample size is below the minimum necessary to apply the theorem