Problem 2: Annual Salary for College Graduates (there is no data file for this problem) A recent study was conducted to investigate if starting annual salaries differ for otherwise comparable graduates from different universities. From a one-year follow up survey from two universities, one university on the east coast and one on the west coast, data were collected for 200 graduates from both schools with the starting annual salary for students who have found employment. Use the following sample statistics to complete this problem. University 1 Sample size, n 200 Sample mean, X $50,900 Sample standard deviation, s $5,900 University 2 200 $49,300 $6,500 a) Define the population parameter of interest in context of this question in one sentence. b) Imagine you were using a hypothesis test to determine if a significant difference exists in the average annual salaries of the graduates between the two universities. State the hypotheses you would use to test this claim. c) Construct the 95% confidence interval in StatCrunch using STATT Stats Two Sample With Summary. Copy and paste the output table into your document. Assume all conditions are met for the CLT. d) Should you reject or fail to reject the null hypothesis in part (b)? Explicitly use your confidence interval from part (c) (and only the confidence interval) to justify your choice in one sentence (do not run this hypothesis test in this part). e) What conclusion can be made in this case? Make sure the conclusion is in one to two sentences and in context of the problem. f) Produce hypothesis test output using STATT Stats Two Sample With Summary. Copy the output into your solutions and state in one sentence whether or not this verifies your decision in part (d). g) Construct the 99% confidence interval in StatCrunch using STAT T Stats Two Sample With Summary. Copy and paste the output table into your document. h) Using the same hypotheses you stated in part (b), what decision and conclusion can be made in this case? Provide an answer and a reason for your choice and use complete sentences for the decision and conclusion. Please only use your confidence interval to answer this question (do not run this hypothesis test in this part). i) Did your decision and conclusion change between parts (d) & (e) to part (h)? Provide in one to two sentences what do you think happened and include a reason.