FACULTY OF INDUSTRIAL SCIENCES & TECHNOLOGY FINAL EXAMINATION

COURSE : APPLIED STATISTICS

COURSE CODE : BUM2413IBSU1023/BCT20531BPF3313/ BKU20321BAM3022/BMM2122

LECTURER : ROSLINAZAIRIMAH BINTI ZAKARIA MOHD RASHID BIN AB HAMID NOR HAFIZAH BINTI MOSLIM NOR AZILA BINTI CHE MUSA NOOR FADHILAH BINTI AHMAD RADI FARAHANIM BINTI MISNI

DATE : 2 JANUARY 2013

DURATION : 3 HOURS

SESSION/SEMESTER : SESSION 2012/2013 SEMESTER I

PROGRAMME CODE : BSB/BSK/BAAJBAEIBCNIBCGIBCSIBPP/ BPTIBPSIBFFIBFMJBKCIBKG/BKB/BMM/ BMI/BMBIBMF/BMA/BEE/BEP/BEC

INSTRUCTIONS TO CANDIDATES 1. This question paper consists of EIGHT (8) questions. Answer all questions. 2. All answers to a new question should start on a new page. 3. All the calculations and assumptions must be clearly stated. 4. Candidates are not allowed to bring any material other than those allowed by

the invigilator into the examination room. EXAMINATION REQUIREMENTS:

1. Statistical Table 2. Scientific Calculator

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

This examination paper consists of TWELVE (12) printed pages including front page.

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QUESTION 1

Define the terms statistic and parameter.(2 Marks)

QUESTION 2

The breaking strength of hockey stick shafts (in Newtons) made of two different graphite-Keviar composites are given in Table 1.

Table 1: Breaking strength of hockey stick shafts

Composite A 487.3 444.5 467.7 456.3 449.7 459.2 478.9 461.5 477.2

Composite B488.5 501.2 475.3 467.2 462.5 499.7 470.0 469.5 481.5

485.2 509.3 479.3 478.0

(a) Find the sample means and variances for the data above.(4 Marks)

(b) Find a 99% confidence interval for the standard deviation of the breaking strength for Composite A.

(5 Marks)

(c) Determine whether the variability of breaking strength for composite A is not more than composite B at 0.01 level of significance.

(7 Marks)

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QUESTION 3

A study is conducted to compare the efficacy of medicine X to treat major depression. 200 outpatients were involved in the study that had been diagnosed with major depression. The patients were equally assigned to two groups randomly. One of the groups received the treatment with medicine X, and the other group received placebo (no treatment). After eight weeks, 19 of the placebo-treated patients showed improvement, whereas 27 of those treated with medicine X had improved.

(a) Construct 94% confidence interval for the population proportion of medicine X. (5 Marks)

(b) Based on the information given, is there any evidence to believe that medicine X has no effect in treating major depression at a 0.05?

(9 Marks)

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QUESTION 4

Table 2 gives the results of an experiment for niacin-contents in peeled and processed

peas. There are three process of granulations (A, B and C) and two kinds of preparations (Ri and R2) involved in the experiment.

Table 2: Niacin-contents

PreparationsGranulations

A B C

Ri 190 171 150 136 146 172

R2 107 115 135 138 97 112

(a) How many factor(s) involved in this experiment? State the factor(s). (2 Marks)

(b) Given SSA(Preparation) = 5676.75, SSB(Granulation) = 394.6667, SSAB = 2166.0000 and MSE = 127.5833, construct and complete the ANOVA

table. Show all the necessary calculations.(12 Marks)

(c) Is there any interaction effect in niacin-contents between preparations and granulation processes at 5% level of significance?

(5 Marks)

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QUESTION 5

A study is conducted to investigate the relationship between blood pressure rise and

sound pressure level. The data of the study are given in Table 3.

Table 3: Blood and sound pressure levels

Blood pressure rise 1 0 1 2 5 4 6 2 (mmHg) Sound pressure level 60 63 65 70 70 80 90 80 (dB)

(a) Identify the independent and dependent variables. (1 Mark)

(b) Calculate the value of correlation coefficient and interpret its value. (9 Marks)

(c) Estimate the regression coefficients and hence write the equation of the estimated regression line.

(5 Marks)

(d) Find the predicted mean rise in blood pressure level associated with a sound pressure level of 100 decibels.

(1 Mark)

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QUESTION 6

A study is conducted to investigate the factors that influence the level of mercury

contamination in 25 different lakes. Water samples were collected from the surface of the

middle of each lake. The alkalinity, pH level, the amount of calcium (mg/1) and chlorophyll (mg/1) were measured in each sample. Then, a multiple regression analysis is conducted to identify the factors that significantly influence the mercury level as shown

in the Excel output below. SUMMARY OUTPUT

Regression Statistics Multiple R 0.72157 RSquare 0.52067 Adjusted R Square 0.42480 Standard Error 0.29177 Observations 25

ANOVAdf SS MS F Significance F

Regression 4 1.8495 0.4624 5.4312 0.0040 Residual 20 1.7026 0.0851 Total 24 3.5521

Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 1.3065 0.4954 2.6373 0.0158 0.2731 23399 0.2731 - 2.3399 Alkalinity -0.0018 0.0055,-0.3302 0.7447 -0.0133 0.0097 -0.0133 0.0097 PH -0.0790 0.0858 -0.9202 0.3684, -0.2581 0.1001 -0.2581 0.1001, Calcium -0.0011 0.0063 -0.1687. 0.8677 -0.0143 0.0121 -0.0143 0.0121 Chlorophyll -0.0033 0.0040 -0.8388 1 0.4115 -0.0116 0.0050 -0.0116 0.0050

Based on the given Excel output of the multiple regression analysis, answer the

following:

(a) What is the different between correlation coefficient and coefficient of determination?

(2 Marks)

(b) Write the regression equation.(3 Marks)

n.

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(c) Interpret the calcium coefficient in the regression equation.(2 Marks)

(d) Predict the level of mercury contamination when alkalinity and pH level are both at level 2 while 10 mg/l of calcium and 5 mg/l of chlorophyll are measured.

(3 Marks)

(e) Test the hypothesis for the regression model based on the given ANOVA table at 5% significance level.

(4 Marks)

QUESTION 7

According to the statistics of the Department of Transportation, the arrival performance by the airlines is shown in Table 4.

Table 4: Percentage of arrival performance

Arrival Performance Percentage of Time On-time arrival 71 Delayed 8 Behind the schedule (late arrival) 9

[Other (because of weather and other condition) 12

A sample of 200 flights for a major airline company showed that 125 planes arrived on-time, 10 were delayed, 25 were behind the schedule and the remainder are due to other reasons. At a = 0.001, do the results differ from the statistics of the Department of Transportation?

(8 Marks)

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QUESTION 8

The sugar concentrations in apple juice measured at 20' C were reported in an article of Food Testing & Analysis for 50 readings in the frequency distribution table below.

Table 5: Frequency distribution of sugar concentration

Class interval 1.0-1.2 1.3-1.5 1.6-1.8 1.9-2.1 1 (sugar concentration) I I I Observed frequency 10 15 15 10 I

At 2.5% level of significance, is there any evidence to support the assumption that the

sugar concentration is normally distributed when 1u = 1.5 and o = 0.5?

(11 Marks)

END OF QUESTION PAPER

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Appendix - Table Of Formulas

Confidence Intervals, Sample Sizes and Hypothesis Testing Confidence intervals for p Hypothesis testing for p.

a - a XZai27= , X+Z7=J ___ Ziest /[ -

X - , X + ZrJ

Ztest =

-

L\X_ta/2v_I= , X+t1 _ sjfl ijfl)

- Xf1 test

where v=n-1 Confidence intervals for A - Hypothesis testing for p -

22

(Yi- X2 ) Za/2+

_(-2)-0 X-1Ziest - +

For a ^ cry: For a ^

_(-2)o f ( 12 2\ 1S1 I I (x

_X2- )Zai2!_+1 IZtest 12 2

l '2

vni fl2) Vi 2

For a ^ a: For U12 ^

_(i-2)-u0 ____

( 12 I Is1 - -test I

Is1 S2 2 (x1 X2 ) tai2 v I 4J+

L Vhhi fl2) V2i 2 1

L 2 2\2

1+l1 2 2'\2

flJ where =

l 2 where v

S1 21 2 1 2 12 y2

W n ) 2 n1 -1 n2-1 n1-1 n2-1

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Forcr =o: For o =or 2

(-)--,u

2)Zai2+ -1- fl ]

Zte

- 2 pn1n

For o- = For a = U2:

_(-2),uo __

-)c,2 SP\/__+_ J , 1 2ttest -

'n1 fl

where V = fl + fl2 2 where v = + n2 2

Pooled estimator, s

f(n-1)s+(n2-1)s -

n+n2-2

Confidence Interval for PD Hypothesis Testing for PD

a XD -9 T' XD + Za/ /2Jn

XD PD test where v=n-1

I'Fn (XD_Za/7,XD+Za/TJ

SD

[XD - ta/,,..1 7=, X + t/,,1

Confidence intervals for ,r Hypothesis testing for ;r

p+ai2(1J

Ztest=ff0)

Confidence intervals for ir, - Hypothesis testing for if1 - if2

(p1_p2)r0 If ifo O, Ztest

K2 7C2

[(Pi_P)Za/2if1(1_if1)+ff2(1_if2) J If if 0, ZtestFPP

(l)[-+_J

+ x2 where p = p

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Confidence intervals for a 2 Hypothesis testing for 0.2

1( 1 ) s2 (n _1)S2 (n1)s2

%a,v Z1a/2,v ) = 2 0.0 where v=n-1

Confidence intervals for0.2

Hypothesis testing for0.2

1 S12 where v1 = n 1 ' faI2,v2 I

Jest - 2 22 V1 S2 far,vi ,v, 2 ) V2 2

1 S2

Sample sizes

[Zai2OJn=p(l_p)(J

Analysis of Variance (ANOVA)

One-way ANOVA Two-way ANOVA

SST =xk_+ x.2 k

SST = x21=1 j=l k=1 a r

a 1

SSA = x2 - f 2 ' N

br '" abr

k x2 1

n N"

r11j1 ar SSE = SST - SS(Tr) SSE = SST - SSA - SSB - SSAB

Goodness of Fit Test and Contingency Tables

Goodness of Fit Test Test using Contingency Tables

E.n.

' xn.

=

k(QE)2

Ej 2 r

Zt2 _

est %I Free distribution DoF; v = ki

E ''

Hypothesized distribution DoF; v = k -

1 where v = (r - 1)(c 1)

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Simple Linear Regression and Correlation

r=.JSXS)Y

(XI)(YIJ ( I Xi n[J2

-

Sx '' - SYY

n 1=1 fl 1=1

Regression line equation: 5' = A + /x where /3j = and fl =j7 - Hypothesis Testing for Intercept, flo Hypothesis Testing for Slope,

fl0 =0 fl1=0

_A-1s0 A t. -

s.e(flo)MS

1+

_I,81= t.

s.e(/)rMSR- 1 S)

v=n-2 vn-2 Sum_of Squares___Regression,_ SSR Mean Square Residual, MS ReS

SSR=/3ISXY MS Res_L_n-2

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