Question 3 A large university claims that the average cost of housing within 3 miles of the campus is S 7200 per school year. A high school student is preparing her budget for her freshman year at the university. She is concerned that the university's estimate is too low. She obtains a random sample of 64 records and computes the average cost is $ 7300 with a standard deviation of S50. a) Part 1 - the p-value approach: Step 1. State the null and alternative hypotheses. Step 2. Write down the appropriate test statistics and justify (check assumptions) Step 3.Calculate the value of the test statistic and p-value A p-value indicates: The probability the null hypothesis is true (ii) The probability that the alternative hypothesis is true (ii) The probability the null hypothesis is true given the observed statistic (iv) The probability of the observed statistic or more extreme given that the null hypothesis is true (v) The probability of the observed statistic or more extreme given that the alternative hypothesis is true Step 4: State your conclusion (in one sentence, state whether or not the test rejects the null hypothesis and in another sentence apply the results to the problem). What type of error could you make in your hypothesis test? Type I error Type II error No er Describe the Type I error (in one or two sentences, in the context of the problem ). What are the consequences of making a Type 1 error? Describe the Type II error (in one or two sentences, in the context of the problem ). What are the consequences of making a Type II error? Part 2: Step 1: The critical value Approach: Write down the rejection of your test. Step 2: State your conclusion Part 3: Calculate an appropriate confidence interval (two sided or lower or upper bond) and explain how it can be used to test the hypotheses b) What is the power of the test (don't calculate, just explain) How could you increase the power of the test? (Circle the right answer) (i) sample size : Increase decrease or or (ii) significance level a: Increase decrease c) Just circle correct statement (general question, not related to this problem) If a hypothesis is rejected at the 0.05 level of significance, it: a. must be rejected at any level b. must be rejected at the 0.02 level c. must not be rejected at the 0.02 level d. may be rejected or not rejected at the 0.02 level