Econ 309Applied Business and Economic Statistics IIMidterm 2Spring Quarter 2014This midterm is due a week from today at the beginning of the class. Please show your work.1. In order to estimate the difference between the average daily sales of two branches of a department store, thefollowing data has been gathered.Downtown Store North Mall StoreSample size n, = 23 days n2 = 26 daysSample mean (in $1,000) Xl =37 X2 =34Sample standard deviation (in $1,000) SI = 4 S2 = 5Develop a test for the difference between the two population means. Let a = 0.05.2. The following sample information is given concerning the ACT scores of high school seniors form two localschools.School A SchoolBni = 14 n:l = 15X = 25 x =23 1 :Iai = 16 0; = 10Develop a test for the difference between the two population means. Let a = 0.01.3. The management of Regional Hospital has made substantial improvements in their hospital and would like totest and determine whether there has been a significant decrease in the average length of stay of their patientsin their hospital. The following data has been accumulated from before and after the improvements. At a=0.05, test to determine if there has been a significant reduction in the average length of stay.After BeforeSample size 45 58Mean (in days) 4.6 4.9Standard Deviation (0″) 0.5 0.6Using a = 0.05, test to see if the average length of stay in RFR is significantly less than theaverage length of stay in GR. Let a = 0.05.4. A random sample of 89 tourists in Chattanooga showed that they spent an average of $2,860 (in a week) witha standard deviation of $126; and a sample of 64 tourists in Orlando showed that they spent an average of$2,935 (in a week) with a standard deviation of$l38. We are interested in determining if there is anysignificant difference between the average expenditures of those who visited the two cities?a. Determine the degrees of freedom for this test.b. Compute the test statistic.c. Compute the critical value(s).d. What is your conclusion? Let a = .05.5. Consider the following hypothesis test:J.lI – J.l2 :::; 0J.ll-J.l2> 0
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