# Applied Business and Economic Statistics II Midterm 2 Spring Quarter 2014 This 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, the following data has been gathered. Downtown Store North Mall Store Sample size n, = 23 days n2 = 26 days Sample mean (in \$1,000) Xl =37 X2 =34 Sample standard deviation (in \$1,000) SI = 4 S2 = 5 Develop 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 local schools. School A SchoolB ni = 14 n:l = 15 X = 25 x =23 1 :I ai = 16 0; = 10 Develop 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 to test and determine whether there has been a significant decrease in the average length of stay of their patients in 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 Before Sample size 45 58 Mean (in days) 4.6 4.9 Standard Deviation (0″) 0.5 0.6 Using a = 0.05, test to see if the average length of stay in RFR is significantly less than the average 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) with a 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 any significant 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 :::; 0 J.ll-J.l2> 0

Applied Business and Economic Statistics II
Midterm 2
Spring Quarter 2014
This 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, the
following data has been gathered.
Downtown Store North Mall Store
Sample size n, = 23 days n2 = 26 days
Sample mean (in \$1,000) Xl =37 X2 =34
Sample standard deviation (in \$1,000) SI = 4 S2 = 5
Develop 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 local
schools.
School A SchoolB
ni = 14 n:l = 15
X = 25 x =23 1 :I
ai = 16 0; = 10
Develop 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 to
test and determine whether there has been a significant decrease in the average length of stay of their patients
in 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 Before
Sample size 45 58
Mean (in days) 4.6 4.9
Standard Deviation (0″) 0.5 0.6
Using a = 0.05, test to see if the average length of stay in RFR is significantly less than the
average 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) with
a 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 any
significant 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 :::; 0
J.ll-J.l2> 0