Problem 3. For many years, the length-of-stay [LOS] for in-patients at St. NoWhere Hospital has averaged 5 days. Due to the increasing popularity of managed care programs, the chief administrator at St. NoWhere believes the mean LOS at the hospital has decreased significantly. To test the administrator's belief, you examine hospital records for a random sample of 25 in-patients who were released last week. The sample data reveal an average LOS of 4.53 days, with a standard deviation of 1.678 days. 3a) State the Null and Alternative Hypotheses associated with the test: (4 points) 3b) What is the calculated value of the associated test statistic? (WORK REQUIRED for CREDIT; 5 points) ANSWER: 3c) What is the critical value of the associated test statistic for a = 0.05 (please show the relevant probability value and degrees of freedom)? (4 points) ANSWER: 3d) State your decision about the null hypothesis. (3 points) FAIL to REJECT HO REJECT HO (please CIRCLE or HIGHLIGHT one) 3e) State your conclusion (meaning, interpret your decision given the context/situation) (3 points) 3f) SET UP, meaning PLUG NUMBERS in to but do NOT solve, the formula to calculate the P-value of this test. (4 points)