MAA 161 - Statistics for Science Students - EPrints USM

(1)

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.

(2)

l.

Given the

following

stem-and-leaf display where the leaf

unit

is equal

tol:

(a)

How many data values are shown on this display?

(b) List

the

first four

data values.

(c)

Find the

first

quartile, mean, median and mode.

[10 marks]

2.

^{The mean}

lifetime of

^{a certain}^tyre

is

^30,000kilometers 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

^aredefined as

follows:

A--the

student selected is

full-time

C

:

the student selected is female

(a)

Are events

A

and C independent?

JustiS

^youranswer.

(b)

Find the

probability

P(A or C).

(c)

Find the

probability

P(A _IC).

[10 marks]

4. If

2%

of

the batteries manufactured

by

a company are defective,

find

the probability that

(a) in

a case

of

20 batteries, there are 3 defective ^ones.

(b) in

a case

of

144 batteries, there are at most

3

defective ones. Use the Poisson approximation

[8 marks]

5.

^The^averagecholesterol 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 the

cholesterol content

will

^be

gr eater than 220

milli

grams.

(b) If a

sample

of 35

eggs

is

selected,

find the probability that the

mean

of

the sample

will

be larger than220 milligrams.

(c) lf l0% of

the eggs contain less than

x milligrams of

cholesterol,

find

the value

ofx.

[2

^marks]

33679 00112245

4555

⁶

00145

45

6 7 8 9

l0

...3t-

(3)

6.

3 IMAA

^161]

A

normal population has a mean

of

38 and a variance

of

16. Samples

of

size

36

are randomly chosen.

(a)

Describe the distribution

of

7

,the

^mean

of

samples

of

size 36.

(b) Find

a value

of k

such that 95Yo

of all

such samples

will

have a mean

x within

the

interval 38-k

^<

x <38+k.

[8 marks]

A

recent study indicated that 40o/o of the 120 women over age 35 were singles.

(a) 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?

(b) If no

estimate

of the

sample

proportion is

available,

how large

should the sample be?

[8 marks]

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.

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

The administrator

of

the college wishes to test whether the scores

in

Mathematics is independent of the scores in English.

State the hypothesis of the test.

Determine the

critical

resion and calculate the value of the test statistic. IJse

a:

0.05.

(c)

7.

8.

(a) (b)

Before 92 110

t02

89 108 98 105 111 96

After

91 108 100 92 106 102 103 106 98

Poor Average Good

(4)

10. The

following

sample data represents the amount

of time (in

hour) spent on outdoor activities per week for 20 students at certain school.

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)

5

APPENDIX

IMAA

¹⁶¹¹

Confidence

Interval

x+

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o

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^",ln

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1,rlna

dr-

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ua

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(i', r,u2v1,' i",,,)

11 -+- n_

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Test Statistic

=- X-p

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tJi

=- X-p

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l4n

=i-oo 'f-

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^Jnd

_b-f,

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=y

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t

//.

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-(p,- pr)

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dk=

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(fl_.H

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b(

(6)

Table

A5

^{Table of}Critical TValues for Wilcoxon's Signed-Ranks and lVlntched-Puirs Signed-Ranlcs Test

On€-taned kvel of slgnlllcame

.05 .$25 .01

^.00s

Two-tnihd levcl of significance

.10 .05 .42

^.0t

One-aafled level of slgnlficance

.0s

^.02s

.01

^.00-5

Trpo-tailed level of significance

.10

^.05

.42

^.0r

t0 l3 l7

25

tt 10 l-a

ta

2l

;

1

J 5

9 t1 1{

19

A

11 )!

37 +J 49 61 69 76 84 92

116 l?6

137

t47 r59

170 182 r95

101 110 120 130 140 l)l t62 r73

91

r00

lltt

109

128 138 14B

r59

171

r82

194 207 220 233

261

tor216

307 322 339 355 373

38 256 n5 ?tr 39 27r U9

2?.4

40 286 264

²³⁸

41 30? 279

^X52

4, 319 294

²⁶⁶

43 336 310

2A1

4 353 377

²⁹⁶

45 37t 343

3r?

46 389 361

328

47 407 378

345

48 426 396

362

49 446 415

3'19

-50 466 134

39'l I

l5 t9 2?,,.f

?t

4tt 5J 6L 68 75 83

2A

130

29

¹⁴⁰

30

l5r

31

¹⁶³

32

^r',75

33

¹⁸⁷

34

²⁰⁰

35

^?13

i6

²²⁷

J7

²⁴¹

208

^t85

'!? ^I 198

50 620 132

aq?

985

3 5 9 r1 t0

11 12

t3 l4

1530?5

16 35

²⁹

t7 41

³⁴

18 47

⁴⁰

19 -53

⁴⁶

20 60

⁵²

2r 67

⁵⁸

22 75

⁶⁵

23 83

⁷³

x4 91

^8r

25 100

⁸⁹

26 ll0

⁹⁸

n ll9

^rc.7

(7)

[MAA

¹⁶¹¹

Rejer;t llte

ltull

h1'peithesis

if

rlre *nrnller numtrcr ^crfpositivu or

n*gutirr

stgns is less thsr: orrc;unl tu

illc vultl* irt

ilrc tirlrh:,

.r\intr'; lirhlu I ^{in frrr}fl|ls-uik.d nr tw'o-t-rri:lsd. rts$. Thr: tcrnilf rcFfl$unls lhu hjquJ nurrrhuc ril prrtitir.c artd. rtcglti$c ripns. Tltc lf5{ }:filuf js lhc ntlm},;r $f L:sn frrr,tur.rtit $i!fis.

.S*ryrrE; Fnlnl-trttu,'nnJnf .{.mr.rlruru-llati.rtilal.;trt-rtt'tir!iu,'t, t'sl. +!'l [1t{6}.

TTF.,tr.:l- fifi. \\r. tr. fJiren ard ts. l'{. l{oo1.

rf

On -tailcd"

ff E

0,{l{}5 flf

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c =

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n = 0.lll n = 0.ll!. n =

^11.05 tn

= ll;l{l

fi g

r0

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t2

ll

lrt

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lfi

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t:

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t

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4 4 4

5

)

fl

0 0 I

I I 7

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{

4 5

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5

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I I I

j

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3 3

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4 5 5 5 6 fi fi

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