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課程名稱︰統計學
課程性質︰系必修
課程教師︰雷立芬
開課學院：管院
開課系所︰國企系
考試日期（年月日）︰2010/4/14
考試時限（分鐘）：3 hr
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1. A test is to be conducte involving the mean holding power of two glues
designed for plastic. First, a small plastic hook has coated at one end with
Epox glue and fastened to a sheet of plastic. After it dried, weight was added
to the hook until it seperated from the sheet of plastic. The weight was then
recorded. This was repeated until 12 hooks were tested. The same procedure
was followed for Holdtime glue, but only 10 hooks were tested. The sample
results, in pounds, were:
Epox Holdtime
_
X 250 252
S 5 8
n 12 10
At the 0.01 level of significance, is there a difference between the mean
holding power of Epox and Holdtime? (15%)
2. To compare the wearing of two types of automobile tires, 1 and 2, an
experimentr chose to "pair" the measurement, comparing the wear for the two
types of tires on each of 7automobiles, as shown below. Determine whether
these data are sufficient to infer at the 10% significance level that the two
types of tires wear differently.(10%)
Auto 1 2 3 4 5 6 7
Tire1 8 15 7 9 10 13 11
Tire2 12 18 8 9 12 11 10
3. Assume that n1=100, X1=45, n2=50, X2=25. At the 0.01 level of significance
is there evidence of a significant difference between the proportion of
successes in group 1 and group 2? (10%)
4. A manufaturer of automobile transmissions uses three different processes.
The manager ordered a study of the production cost to see if there is a
different among the three processes. A summary of the finding is shown below.
Process1 2 3 total
Process Total($100's) 137 108 107 352
Sample size 10 10 10 10
Sum of Squares 1,893 1,188 1,175 4,256
a) set up the null hypothesis and the alternative hypothesis (5%
b) What is the variance explained by the different processes? (5%
c) What is the variance unexplained bt the different processes? (5%
d) Complete the ANOVA table (8%
e) What is your conclusion for the test? (2%
5. The vice president for marketing recently recruited 20 outstanding college
grduates to be trained in sales and management. The 20 individuals are random-
ly assigned, 10 each, to one of two groups. A "traditional" method of training
(T) is used in one group and an "experiment" method (E) in the other. After
six months on the job, the vice president ranks the individuals on the basis
of their performance from 1(worst)to 20(best). Is there any evidence of a
difference in performence based on the two methods? (10%)
T 1 2 3 5 9 10 12 13 14 15
E 4 6 7 8 11 16 17 18 19 20
6. A nationwide market research study is endertaken to determine the
perferences of varius are groups of males for different team sports. A random
sample of 1000 men is selected, and each individual is asked to indicate his
favorite team sport. the results are as follow:
Age Group Baseball Football Basketball Hockey Total
Under20 26 47 41 36 150
20-29 38 84 80 48 250
30-39 72 68 38 22 200
40-49 96 48 30 26 200
50and over 134 44 18 4 200
Total 366 291 207 136 1000
At the 0.1 level of significane, is there evidence of a significant relation-
ship between men's age and their preferences in sports? (15%)
7. Because of the cost of producing television shows anf the profits associated
with successful shows, television network executives are keenly interested in
public opinion. A network has recently developed three comedy series. The
pilot of each series is shown into 10 randomly selected people who evaluate
wach show on a 9-point scale where 1=teriible and 9=excellent. The results
are shown below. Can we infer that at the 5% significance level that differ-
ences exist among the show's evaluations? (15%)
Person show1 show2 show3
1 6 4 7
2 5 4 5
3 7 6 8
4 7 7 8
5 9 9 9
6 5 7 6
7 4 4 5
8 6 3 7
9 5 6 6
10 7 7 8
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