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

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