MGMT2263
Worksheet #3
1)
A
builder conducted a study in a major city in which the city was divided into
different regions. One of the regions had a higher percentage of senior
citizens than other regions of the city. He was concerned that the age standard
deviation in this region might be less than in the others. The sample size of
this region is 16 and the age standard deviation is 5.3 years. In another
region chosen at random, the sample size is 13 and the age standard deviation
is 7.2 years. Based on this evidence, is the age standard deviation in the
first region significantly less than that of the second region? Test at a 5%
level of significance.
(F = 1.8455; conclude the standard deviation
for the region with the high percentage of seniors is not significantly less
than that of the other region)
2)
Sales
from two stores were gathered. Analysis of the data indicated both samples were
normal. The summary statistics from the stores are:
|
Sample size |
Mean |
Std. Dev. |
|
|
Store 1 |
9 |
45 |
4.1 |
|
Store 2 |
10 |
48 |
9.2 |
Is there any significant difference in the
standard deviations of the stores’ sales? Test at a 5% level of significance.
(F = 5.0351; conclude the standard deviations are not equal)
3)
A
manufacturer is conducting a test of the tensile strengths of two types of
copper coils. The summary statistics are:
|
Sample size |
Mean |
Std. Dev. |
|
|
Coil A |
9 |
118 |
17 |
|
Coil B |
16 |
143 |
24 |
The tensile strengths are approximately normally
distributed. Is there any significant difference in the average strengths of
the two types? Test at a 5% level of significance. (t = 2.7496; conclude the
average strengths of the two types are not equal)
4)
Is
there a level of significance between 1% and 10% in which the opposite verdict
would have been reached? (if the level of significance were set at 1%, the
critical value would be 2.807 and the opposite conclusion would have been
reached)
5)
Construct
a 95% confidence interval of the mean difference in tensile strengths of the
two types of coil. What conclusion would you reach
based on the results of the confidence interval? (6.1881 < mB - mA < 43.8119; we would reject Ho since the
hypothesized difference of 0 does not fall in the confidence interval)
6)
Let
us return to the data from question 2 and test if there is any significant
difference in the average sales of the 2 stores. Assume that both data sets are
normally distributed. Do not assume a level of significance. (t = 0.9333;
p-value > 10%; conclude no significant difference in average sales of the 2
stores)
7)
A
business magazine compared bonuses for 10 executives for the years 2006 and
2007. These were the results (in thousands of dollars):
|
CEO |
2006 Bonus |
2007 Bonus |
|
#1 |
195 |
196 |
|
#2 |
183 |
160 |
|
#3 |
208 |
220 |
|
#4 |
190 |
195 |
|
#5 |
220 |
200 |
|
#6 |
235 |
250 |
|
#7 |
175 |
180 |
|
#8 |
150 |
145 |
|
#9 |
245 |
240 |
|
#10 |
210 |
230 |
Analysis of the data indicated they are normally
distributed. Is there any significant difference in the average bonuses of the
two years? Test at 5%.
(t = 0.1119; conclude there is no significant
difference between the two years)
8)
Construct
a 95% confidence of the difference between the two years. Round the limits to
the nearest hundred. Interpret the interval. Why would the same conclusion be
reached? (–9,600 < m(2007) - m(2006) < 10,600; we would not
reject Ho since the hypothesized difference of 0 falls in the confidence
interval)
9)
Suppose
a level of significance had not been chosen. Why would the same conclusion be
reached? (do not reject Ho since p-value > 10%)
10)
A
law firm wants to know if there is a difference in the number of typing
mistakes made by two secretaries in the firm. Each secretary was given 5
randomly selected documents to type. The results were:
|
Secretary A |
3 |
5 |
4 |
2 |
0 |
|
Secretary B |
2 |
0 |
4 |
3 |
1 |
No assumptions about the normality of the data
were made. Test at a 5% level of significance. (T = 24; no significant
difference)
11)
A
psychologist conducts a seminar to increase a person’s self-esteem. A
before-and-after test that measures a person’s self-esteem was given to nine
randomly selected individuals. The results were:
|
#1 |
#2 |
#3 |
#4 |
#5 |
#6 |
#7 |
#8 |
#9 |
|
|
Before |
70 |
72 |
75 |
61 |
82 |
55 |
43 |
51 |
84 |
|
After |
74 |
88 |
71 |
62 |
89 |
58 |
41 |
63 |
80 |
No assumptions about the normality of the data
were made. Is the seminar’s method effective? Test at a 5% level of
significance. (T- = 12; conclude method not effective)
From the textbook:
9.20 (page
279). Note: Do the F test first to determine the correct formula.
9.28 (page
283)
9.59 (page
296)
13.12 (page
513)
13.19 (page
516)