The data below are the responses (in dollars) from a simple random sample of MTH 120 students to the question, "How many dollars per week do you spend eating out?" 10 25 50 12 25 12 30 60 60 15 30 75 20 30 80 20 30 80 20 40 20 40 20 40 20 40 25 40 25 50 25 50 a. State the null and alternative hypotheses. You must choose a left-tailed, right-tailed, or two-tailed test to perform, and explain why you chose that type of test. (5 pts, must have correct mathematical notation and include a sensible explanation.) b. Verify that the three conditions are met in order to run the hypothesis test for the population mean. Explicitly state the three conditions, and show the work that verifies them. (5 pts) c. Determine which distribution to use for the test statistic, and state the level of significance you are choosing to use. Explain why you needed to use that specific distribution. (5 pts, must have correct mathematical notation and include a sensible explanation.) d. Gather data and calculate the necessary sample statistics. (Use the project 3 sample data supplied in class/D2L.) Calculate the test statistic. Note: you will need to calculate certain statistics from the sample data to calculate the test statistic. Show all work (5 pts, must have correct mathematical notation) e. Find the P-value. Show all work. Explain what the meaning of the P-value is in this context. (5 pts, must have sensible explanation) f. Make a decision. Show the statistical reason why you made the decision that you did. (3 pts) g. State the conclusion of the test for this specific context. (5 pts) h. After you run your test, let's assume later you find out that the true population mean is that MTH 120 students spend a mean of $40 per week eating out. Based on your conclusion in part (f), did you make a Type I error, a Type II error, or a correct decision? Explain. (5 pts, must have a sensible explanation)