Exercise 1
1.
In order to estimate the difference between the average yearly salaries of top managers in
private and governmental organizations, the following information was gathered.
Sample Size
Sample Mean (in $1,000s)
Sample Standard Deviation
(in $1,000s)
Private
50
90
Governmental
60
80
6
8
Develop an interval estimate for the difference between the average salaries of the two
sectors. Let  = .05.
Answer:
$7,380 to $12,620
2.
A recent Time magazine reported the following information about a sample of workers in
Germany and the United States.
Average length of workweek (hours)
Sample Standard Deviation
Sample Size
United States
42
5
600
Germany
38
6
700
We want to determine whether or not there is a significant difference between the average
workweek in the United States and the average workweek in Germany.
a. State the null and the alternative hypotheses.
b. Compute the test statistic.
c. Compute the p-value. What is your conclusion?
Answers:
a. H0: U - G = 0
Ha: U - G  0
b. Test statistic z = 13.1
c. p-value is almost zero; reject Ho
3. Consider the following results for two samples randomly taken from two populations.
Sample Size
Sample Mean
Sample Standard Deviation
Sample A
20
28
5
Sample B
25
22
6
a. Determine the degrees of freedom for the t distribution.
b. At 95% confidence, what is the margin of error?
c. Develop a 95% confidence interval for the difference between the two population
means.
Answers:
a. 43
b. 3.38 (approximate to df=40 then t(0.025)= 2.021
c. 2.62 to 9.38
4.
The Dean of Students at UTC has said that the average grade of UTC students is higher than
that of the students at GSU. Random samples of grades from the two schools are selected,
and the results are shown below.
Sample Size
Sample Mean
Sample Standard Deviation
UTC
14
2.85
0.40
GSU
12
2.61
0.35
a. Give the hypotheses.
b. Compute the test statistic.
c. At a 0.1 level of significance, test the Dean of Students' statement
Answers:
a. H0: 1 - 2 = 0
Ha: 1 - 2 > 0
b. t = 1.614
c. p-value is between .05 to .1, reject H0
5. The following information was obtained from matched samples regarding the productivity of
four individuals using two different methods of production.
Individual
1
2
3
4
5
6
7
Method 1 Method 2
6
8
9
5
7
6
7
5
8
6
9
5
6
3
Let d = Method 1 - Method 2. Is there a significant difference between the productivity
of the two methods? Let  = 0.05.
Answer:
H0: d = 0
Ha: d  0
Test statistic t = 2.54, p-value is between .02 and .05; reject H0