Download MAA 161 - Statistics for Science Students

UNIVERSITI SAINS MALAYSIA
Kolej Legenda
First Semester Examination
Academic Session 200812009
November 2008
MAA 161
-
Statistics for Science Students
Duration : 3 hours
INSTRUCTIONS TO CANDIDATE:
.
.
Please ensure that this examination paper contains TEN questions in SEVEN
printed pages before you begin the examination.
Answer ALL questions.
On each page, write only your lndex Number.
...21-
2
l.
Given the following stem-and-leaf display where the leaf unit is equal
1611
tol:
33679
00112245
4555 6
00145
6
7
8
9
45
l0
(a)
(b)
(c)
IMAA
How many data values are shown on this display?
List the first four data values.
Find the first quartile, mean, median and mode.
[10 marks]
2.
The mean lifetime of a certain tyre is 30,000 kilometers and the standard deviation is
2,500 kilometers.
(a) If we assume that the distribution is bell-shaped, what percentage of all such
tyres will last more than22,500 km?
(b) If we assume nothing about the shape of the distribution, approximately what
percentage of all such tyres will last between 22,500 and 37,500km?
[10 marks]
3.
One student is selected at random from a group of 200 students known to consist of
140 full-time (80 female and 60 male) students and 60 part-time (40 female and 20
male) students. Events A and C are defined as follows:
A--the student selected is full-time
C : the student selected is female
(a) Are events A and C independent? JustiS your answer.
(b) Find the probability P(A or C).
(c) Find the probability P(A I C).
[10 marks]
4. If 2% of the batteries
manufactured by a company are defective, find the probability
that
(a)
(b)
in
a case
of
20 batteries, there are 3 defective ones.
in a case of 144 batteries, there are at most 3 defective ones. Use the Poisson
approximation
[8 marks]
5. The average cholesterol content
of a certain brand of eggs is 215 milligrams and the
standard deviation is 15 milligra,ms. Assume that the variable is normally distributed.
(a) If a single egg is selected, find the probability
(b)
(c)
the cholesterol content will be
milli grams.
If a sample of 35 eggs is selected, find the probability that the mean of the
sample will be larger than220 milligrams.
lf l0% of the eggs contain less than x milligrams of cholesterol, find the value
gr eater than 220
ofx.
[2
marks]
...3t-
3
6.
IMAA 161]
A normal population has a mean of 38 and a variance of 16. Samples of size 36
are
randomly chosen.
(a)
(b)
Describe the distribution of 7 ,the mean of samples of size 36.
Find a value of k such that 95Yo of all such samples will have a mean
the interval 38-k < x <38+k.
x
within
[8 marks]
7.
A recent study indicated that
(a)
(b)
40o/o
of the 120 women over age 35 were singles.
How large a sample must be taken to be 95o/o confident that the estimate is
within 0.10 of the true proportion of women over age 35 who are singles?
If no estimate of the sample proportion is available, how large should the
sample be?
[8 marks]
8.
A
manufacturer of a new drug claimed that the drug could effectively reduce the
diastolic blood pressure. An experiment was designed to estimate the reduction in
diastolic blood pressure using a sample of 9 people. The following data shows the
diastolic blood pressure readings of these 9 people before and after consuming the
drugs for two weeks.
Before
92
110
t02
After
91
108
100
89
92
108
98
105
111
96
106
102
103
106
98
Perform an appropriate statistical test to test the claim that the drug could effectively
reduce the diastolic blood pressrre assuming that the diastolic blood pressure
readings are normally distributed. Use a: 0.05.
[12 marks]
9. The applicants
for a certain course at a private college are given the Mathematics and
English tests. They were then grouped into one of three categories, Poor, Average and
Good based on their score in the tests. The number of applicants based on these
categories is shown the table below.
Mathematics
Poor
Average
Good
The administrator of the college wishes to test whether the scores in Mathematics is
independent of the scores in English.
(a)
(b)
(c)
State the hypothesis of the test.
Determine the critical resion and calculate the value of the test statistic. IJse
0.05.
State the decision and conclusion.
[2
a:
marks]
...4t-
4
IMAA
1611
following sample data represents the amount of time (in hour) spent on outdoor
activities per week for 20 students at certain school.
10. The
tt.2 r2.r
12.5 I1.8 10.6
13.2 t2.4 10.8 rr.6 r3.7
9.8 10.8 12.6 r2.l 13.0
11.3 t2.4 13.1 12.4 11.6
At a = 0.05, test the hypothesis that the median amount of time (in hour) spent on
outdoor activities per week is 12 hours.
[0
marks]
...5/-
IMAA 1611
5
APPENDIX
Confidence Interval
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...6/-
6
Table
A5
IMAA 1611
Table of Critical TValues for Wilcoxon's Signed-Ranks
and lVlntched-Puirs Signed-Ranlcs Test
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One-aafled level of slgnlficance
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29
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40
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52
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19 -53
20 60
2r
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22 75
23 83
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25 100
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Trpo-tailed level of significance
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30
31
32
33
34
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38
39
40
41
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116
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170
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286
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319
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264
279
294
336
353
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389
407
426
446
466
310
377
343
361
378
396
415
134
200
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207
238
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220
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261
296
233
216
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328
345
307
322
362
339
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355
39'l
373
...7t-
[MAA 1611
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