I Universiti JMalaysia PAHANG EnfleeYIfl - Qfewftcy

FACULTY OF INDUSTRIAL SCIENCES & TECHNOLOGY FINAL EXAMINATION

COURSE : APPLIED STATISTICS

COURSE CODE : BUM2413IBSU1023IBCT2053'3313' BKU20321BAM3022/BMM2122

LECTURER : AZLYNA BINTI SENAWI FARAHANIM BINTI MISNI NOR AZILA BINTI CHE MUSA NORYANTI BINTI MUHAMMAD NOOR FADRILAH BINTI AHMAD R&D! ROSLINAZAIRIMAH BINTI ZAKARIA SITI ROSLINDAR BINTI YAZIZ

DATE 04 JANUARY 2012

DURATION 3 HOURS

SESSION/SEMESTER : SESSION 2011/2012 SEMESTER I

PROGRAMME CODE : BSB1BSKAA/BAE[BCN1BCGi'BCS/BPP'BPT/ BPSfBFFfBFMfBKC1BKG/BK ME/ BMF/BMA/BEE/BEPLBEC

INSTRUCTIONS TO CANDIDATES

1. This question paper consists of SEVEN (7) questions. Answer ALL the 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 TEN (10)printed pages including front page.

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QUESTION 1

A study on an operating system for a portable computer has been carried out thoroughly to estimate the mean and variance of response time. A random sample of six portable

computers from Brand A and a random sample of nine portable computers from Brand B

are chosen. The recorded data (in milliseconds) for both brands are as follows.

Brand A: 25 23 22 25 23 24

Brand B: 28 24 25 26 23 2726 24 25

By assuming that the response time follows normal distribution,

(a) construct a 95% confidence interval on the ratio of variances for both brands of portable computer.

(7 Marks)

(b) test the hypothesis whether the variance response time for portable computer from Brand A is smaller than the variance response time for portable computer from

Brand B at 0.05 level of significance using the traditional method. Based on the

analysis, which brand of portable computer should be chosen? State your reason.

(10 Marks)

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QUESTION 2

Two extrusion machines that manufacture steel rods are being compared. In a sample of 1000 rods taken from Machine X, 930 rods met specifications regarding length and

diameter. In a sample of 600 rods taken from Machine Y, 570 rods met the specifications.

Machine Y is more expensive to run, so it is decided that Machine X will be used unless

it can be convincingly shown that Machine Y produces a larger proportion of rods

meeting specifications.

(a) Find a 99% confidence interval on the difference between two proportions of rods meeting specifications for both machines.

(5 Marks)

(b) Conduct a necessary analysis at 1% significance level for making the decision as to which machine to use. Based on the analysis, which machine should be used?

(Note: Use the traditional method of hypothesis testing)

(8 Marks)

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QUESTION 3

Ahmad and Jasonprepare a report to an engineer in a textile mill who studies the effects

of temperature and time in a process involving dye on the brightness of a synthetic fabric (brightness is measured on a 50-point scale). Three observations were taken at each combination of temperature and time.

Temperature (F) Time (cycles) 350 375 I 400

40 38, 32, 30 37, :35, 40 36, 39, 43

50 40, 45, 36 39, 42, 46 39, 48, 47

The results of the analysis of variance are summarized as follows.

Source of variation SS d.f MS F Time 150.222

Temperature 80.778

Interaction 3.444

Error 186.000

Total 420.444

(a) Completethe ANOVA table. (8 Marks)

(b) At a = 0.05, conduct an analysis of variance (ANOVA) for the given data.

(15 Marks)

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QUESTION 4

Mechanical engineers, testing a new arc-welding technique, classified welds both with

respect to appearance and an x-ray inspection.

- Appearance

Bad Normal Good Total

Bad 20 7 3 30

Normal 13 51 16 80 X-ray

Good 7 12 21 40

Total 40 70 40 150

Test for independence at 5% significance level and show all calculations in three

decimal places.

(8 Marks)

QUESTION 5

Acme Toy Company prints baseball cards. The company claims that 30% of the cards are

rookies, 60% veterans, and 10% are All-Stars. The cards are sold in packages of 100. Suppose a randomly selected package of cards has 50 rookies, 45 veterans, and 5 All-

Stars. Is this consistent with the Acme's claim? Use a 0.1 level of significance.

(8 Marks)

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QUESTION 6

A fast-food chain decided to carry out an experiment to assess the influence of advertising expenditure on sales. Different relative changes in advertising expenditure,

compared to the previous year, were made in eight regions of the country, resulting

changes in sales levels were observed. The accompanying table shows the results.

Increase in advertising expenditure (%) Increase insales(%) 2.4 7.2 10.3 9.1 10.2 I 4.1 7.6 3.5 1

(a) Compute the value of the correlation coefficient for the above data. (9 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 percentage increase in advertising expenditure and the percentage increase in sales, find the

equation of the regression line for the data.(5 Marks)

(d) Estimate the percentage increase in sales when the percentage increase in advertising expenditure is 20%.

(2 Marks)

(e) Explain your answer in part (d).(1 Mark)

n.

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QUESTION 7

A study is conducted to assess the quality of staffs in a company based on their quality of letters of recommendation. There are three predictor variables used to determine the

quality of letters of recommendation, namely college GPA, high school GPA and TOEFL total. The following Excel output shows a multiple regression analysis when all the three

predictor variables are used to predict the quality of letters of recommendation.

SUMMARY OUTPUT

Regression Statistics 'Multiple R 0.6304 R Square . 0.3974 . Adjusted R Square 0.3785 Standard Error 1.17891 Observations 100.

ANOVA'Significance

df MS F

Regression 3 87 9735 29.3245 211005 1.3967E-10.

Residual 96 .- ...........133.4165 1 - ....... 1.3898 - . - ------ ----- 1- ........................... Total 99 221.39001

Coefficients Standard tStat P-value ..

Lower 95% .Upper 95%

Lower 95.0% 1

Upper 95.0% Error

2.8793 0.5760 - 4.9991 0.0000 1.73360 -- 405 - 1.7360 1 4.0225 Intercept -- College GPA

--

0.0907 0.2039 0.4449 0.674 -0.3140 - 095 -0.3140 j 0.4955 -. - High school GPA 13192 02000 65967 00000 09222 17161

09222 17161

:TOEFL total -0.0006 0.0007 1 -0.8616 0.3911 -0.0019- 0.0007 -0.0019 0.0007

(a) State the Coefficient of Multiple correlation, R for this study andinterpret

thisvalue.(2 Marks)

(b) Write the multiple regression equation. (2 Marks)

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(c) Interpret theintercept value and the coefficient of TOEFL total when the other variables are remained constant.

(2 Marks)

(d) Ata = 0.02,can we conclude that neither of the independent variables is related to the dependent variable?

(5 Marks)

(e) State the value of coefficient of determination and interpret this value.

(2 Marks)

END OF QUESTION PAPER

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APPENDIX - Table of Formulas

Confidence Intervals, Sample Sizes and Hypothesis Testing

Confidence intervals for p,

a - a X+1 sJfl Jfl

Xtai2 , n_i , X+ta/2,n_IT) (,k Zal2 , X+Za/2T

Confidence intervals for p 1 -

p

(fCj X-2 Za/2 J^ t^ )

ForFor a1 = a2.

FL

)ZaI2 S+

For a1 a2: For a1 = a2:

2) ta/2v_:_] )ta/2ni+2 S ]

1!i_+.- where v = 2

(

n22)2

n1 -1 n2-1

Pooled estimator, S

= f_1)s+(n2-1)s SP +r2 2

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Confidence intervals for p r H Confidence interals for p1 -

[_Za/2 , +Za/2 J Fn n_ 2 Confidence intervals for a 2 Confidence intervals for cr1 /o

((n_l)s2 (n_l)s2') (2 1 52 ' 'I2,n2-I,n1-1

I ,2 ' ,2 I ita/2,n-I L1-a/2,n-1)2 2 S2 a/2,n1-1,n2-1 S2

Sample sizes :

(Zai2OJ2 2

n P) Za/2 )

Analysis of Variance (ANOVA), Goodness of Fit Test and Contingency Tables

Goodness of Fit Test Two-way ANOVA a b n

SST= xk--X2 k(OE)2 abn 2-

1=1 j=l k=1 Ztest

1=1 Li I

where v = kii2 X2 SSA

bn j1 abn

1 b 1 SSB=x2.--X2

an ' abn n.xn. 'i

R-E I JLL

i a b 2 -ssAB=_x,_x2-SSA-SSB

i=1 j1 n 1=1 3=1abn

--7 SSE = SST _SSA-SSB-SSAB where v=(R-1)(C-1)

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