bum2413 - applied statistics

I1 Universiti Y

Malaysia - PAHANG

Engineering ;l Creativity

FACULTY OF INDUSTRIAL SCIENCES & TECHNOLOGY FINAL EXAMINATION

COURSE : APPLIED STATISTICS

COURSE CODE : BUM2413

LECTURER : NORYANTI MUHAMMAD AZLYNA SENAWI

DATE : 8 NOVEMBER 2010

DURATION : 3 HOURS

SEMESTER : SESSION 2010/2011 SEMESTER I

PROGRAMME CODE : BFF/BFM

INSTRUCTIONS TO CANDIDATE:

1. This question paper consists of SEVEN (7) questions. Answer ALL questions.

2. Write your answers in the answer booklet provided. 3. Answer EACH question on a new page. 4. All calculations and assumptions must be clearly shown.

EXAMINATION REQUIREMENTS:

1. Statistical Tables and Formula 2. Scientific Calculator

DO NOT TURN THIS PAGE UNTIL YOU ARE TOLD TO DO SO

This examination paper consists of NINE (9) printed pages including the front page.

CONFIDENTIAL BFF/BFMI1O1 111BUM2413

QUESTION 1

UMP Human Resources and Management Department doing a survey of newspaper read by non academic staff. The staffs are randomly picked for the survey and the data are

summarized as follows.

Newspapers Number of staffs

Berita Harlan 30

Kosmo 42

New Straits Times 15

--The Star

--7:20:::l

(a) What is the population for the study? (1 Mark)

(b) Determine the technique of collecting data used in this survey. (1 Mark)

QUESTION 2

Two different brands of latex paint are being considered for use. Drying time in hours is being measured on specimen samples of the use of the two paints. Fifteen specimens for

each were selected and the drying times are given as follows.

Paint A

3'S 7 94:

1.7 3.3 5.2 4.2 2.9 T1 4P34

--.

Paint B

5.3 4.3 6.0 5.2 3.7 i S4:4.

Assume the drying time is normally distributed withal =

Find a 95% confidence

interval for the difference of the true average drying time between the two brands of

paints.(11 Marks)

CONFIDENTIAL BFFIBFM/101 111BUM2413

QUESTION 3

Past data indicate that the variance of measurements made on sheet metal stampings by experienced quality inspector is 0.15 square inch. Such measurements made by an inexperienced inspector could have too large variance perhaps because of inability to read instruments properly or too small variance perhaps because unusually high or low measurements are discarded. A new inspector measures a random sample of 80

stampings with a variance of 0.10 square inch.

(a) Test a hypothesis testing at 0.01 level of significance whether the new inspector is making satisfactory measurements. Assume normality.

(8 Marks)

(b) Construct a 95% confidence interval for the true standard deviation of measurements made on sheet metal stampings by new inspector.

(5 Marks)

QUESTION 4

Samples of peanut buffer produced by three different manufacturers were tested for

sodium content (measured in mg), with the following results:

Sodium content Mean Variance

Brand 2.5 8.3 3.1 4.7 7.5 6.3 5.40 5.56 A---

Brand 4.5 3.8 5.6 7.2 3.2 2.7 4.50 2.78 B Brand 5.3 3.5 2.4 6.8 4.2 3.0 4.20 2.63 C

Is there a significant difference in the mean amounts of sodium content in these

samples? Use a = 0.05(15 Marks)

3


QUESTION 5

A group of researchers conducted two-factor experiment used to investigate the effect of pH and catalyst concentration on product viscosity (measured in centistokes). The data are as follows.

pHCatalyst Concentration

25 27 5.6 192, 199, 189, 198 178, 186, 179, 188 5.9 185, 193, 185, 192 197, 196, 204, 244

(a) The ANOVA summary table for the above data is shown below.

Source of variation SS df MS F pH 473.063 473.063 3.230 Catalyst Concentration 95.063 1 Interaction 1 1105.563 7.550 Error 1757.250 Total 3430938 15

Fill in the missing entries.(6 Marks)

(b) At a 0.05 , test is there an interaction effect between pH and catalyst concentration on product viscosity.

(5 Marks)

rd


QUESTION 6

A study of seat belt users and nonusers yielded a randomly selected sample data summarized in the following table. At a = 0.1 significance level, test the claim that the

amount of smoking is independent with seat belt use.

Number of Cigarettes Smoked per Day 1-14 l5 and over

Wear seat belt E175 20 48

Don't wear seat belt 149 17 50

(14 Marks)

5


QUESTION 7

In an experiment, the masses (in grams) of potassium bromide dissolved in 100 grams of water were recorded at temperature raised from 10C.

Temperature (C) Mass (gram) 10 61 20 64 30 70 40 73 50 78

(a) Compute the value of the correlation coefficient for the above data. (8 Marks)

(b) What can you conclude from the value of the correlation coefficient obtained from part (a)?

(1 Mark)

(c) Assuming that there is a significant linear relationship between the temperature 100 grams of water and the mass of potassium bromide, find the equation of the

regression line for the data.(3 Marks)

(d) Estimate the mass of potassium bromide will dissolve in 100 grams of water at temperature 35C.

(2 Marks)

END OF EXAMINATION PAPER

CONFIDENTIAL BFFIBFMI1011IIBUM2413

APPENDIX - Table of Formulas

Confidence Interval & Hypothesis Testing for one Population

X Z/ fest

[-2fl)

[Za r,Ziest=P /n)

=[x t/ ni 'esfXrn

x I Z JiiT1 z - where 3 - and =1 " )

(n-1) s (n-1)s2 ') 2 - (n _1)s2 ' 2 Zia,,ni)

2 Co

Confidence Interval & Hypothesis Testing for Two Populations

I ' fl 2)Po +

12-

Unequal variance

yfl1S2 5EI

fl2) Ii+4

Unequal variance

L2 2tsj (XI-2)-0 where ,

_a/ 12 52 +

fni n2

S12 2 1+2 - n1 '2 v_

ILi I2 W L2) n1 -1 n2-1

7

CONFIDENTIAL

BFFIBFMI101 1UBUM2413

Equal variance[ 1 i

2(-2) )z,,iS =

\1n1 n2

Equal variance

Fn,+

(i-2)i'02)t,1S )F^+SP

n 1)s +(n2 1)s SP

=

+n2 2

where and =1 [C1-2)Zai FI

AP2q2(1-2) p,

Z11

2 ) Pn,

n

2

(1) If p0 0, 2 = whereP^ +n2

VPP PP)

1n2 In1 I S2

',n1-1,n2-1 22 S2

One Way ANOVAContinencv Tables

SST = x i_x2 1=1 j=I

SS(Tr) =1

1 _E X2 __X2 n 1 ' N"

.SSE = SST SS(Tr)

Goodness of Fit

(o1E1)2

1=1 E1

ni x n. and

J n

R c (n..E..) 2 Ii

1=1 j=I .L,

Simple Linear Regression

Refer to Statistical Tables and Formulae


Two Way ANOVA

SST=>xk 1=1 j1 k=1 abn

SSA =x'

2 __ix2 bn i=1 abn

SSA = x2. - x2 an abn

SSAB=1 > x SSA SSB n i=1 j1 a n

SSE = SST SSA SSBSSAB

Page 1Page 2Page 3Page 4Page 5Page 6Page 7Page 8Page 9

bum2413 - applied statistics

Documents