Engineering Statistics SSE2193_Final_Sem1_0607

7/27/2019 Engineering Statistics SSE2193_Final_Sem1_0607

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Sample Final Sem 1 06/07 SSE2193/SSM3763

Answer All Questions

1. From previous record, 15% of all computers supplied by Compter to all governmentagency were defective. 100 computers are selected at random. What is the

probability that the sample proportion of defective computers is between 11% and

17%. [5 marks]

2. The weights of all balls used for State Cup 2005, X1, are normally distributed with

mean 435 grams and standard deviation 15 grams. The weights of all balls used

for Universe Cup 2006, X2, are also normally distributed with mean 440 grams

and standard deviation 10 grams. A random sample of size 40 is taken from eachpopulation. What is the probability that the difference between these two sample

means are less than 10 grams [5 marks]

3. The calcium content in a wholemeal bread is normally distributed, and the variance

calcium content is thought to be 2 = 14.5 mg2. A random sample of n = 20

wholemeal breads is selected. The sample standard deviation of the calcium content

is s = 5.2 mg. Test, at = 0.05 significance level, whether the true variance of

calcium content is 14.5 mg2. [5 marks]

4. 11 pieces of flint were collected from two areas, A and B, and ordered according to

the level of hardness measured by the total degree of damage when two pieces are

rubbed against each other (the lesser the degree of damage is, the harder will the

flint be). The ordered data are as follows:

Origin of flint Degree of damage (%)

A 2.0

A 3.1B 3.2

B 3.4

B 3.6

B 3.7

A 4.1

A 443.6

B 5.2

A 5.4

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8. A research is carried out to improve the design of the sitting position of the pro-

duction operators. The functional arm reach of production operators is a necessary

measurement in the design. In a pilot study, a researcher made this measurement

on two random samples of 8 operators each. The results, in mm, were as follows:

Sample A 705 673 687 6625 700 655 645 663

Sample B 695 703 686 655 703 715 650 665

Assuming a normal distribution for functional arm reach,

a. show that, at = 0.10 significance level, the hypothesis on 2A = 2B should

not be rejected. [6 marks]

b. and using the result in part (a) above, test at = 0.05 significance level

whether there exists a significant difference between the two functional arm

reach of the operators. [6 marks]

9. a. A random sample of 10 metal rods is taken from machine A. The sample

mean diameter is 1.005 cm and the standard deviation is 0.03 cm. Assume the

diameters of the rods are normally distributed. Construct a 99% confidence

interval for the true mean diameter of the metal rods. [5 marks]

b. Another random sample of 13 metal rods is taken from machine B. The samplestandard deviation of the diameter is 0.04 cm. Construct a 98% confidence

interval for the ratio of the true standard deviations of the diameter of the

rods produced by machine A and machine B. [8 marks]

10. A manager wants to investigate the effects of three different training approaches

on the fitness of his players. The following data show the time (in minutes) set

by his players for 4 km running test after the training camp using three different

approaches.

Training approaches

First method Second method Third method

12.3 11.9 10.7

11.7 12.5 11.1

12.7 11.5 10.6

11.4 11.8 12.0

12.5 11.9 11.0

12.6 11.7 12.212.2 11.5 10.9

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a. Perform a one way analysis of variance at = 0.05 significance level to test

whether the different training approaches give the same effect on the playerss

fitness. [11 marks]

b. State the appropriate model and necessary assumption for using the above sta-tistical technique. [2 marks]

11. A study on the amount of rainfall and the quantity of removed air-pollution-caused

particles produces the following data:

Daily Rainfall, x Removed Particles, y

(0.01 cm) (meg/cum)4.3 126

4.5 121

5.9 116

5.6 118

6.1 114

5.2 118

3.8 132

2.1 141

7.5 108

5.5 105

4.8 112

5.4 102

Given Sxx = 19.6692, Syy = 1378.2500, and Sxy = 133.3250.

a. Estimate the regression line to predict the amount of removed particles from

the amount of daily rainfall. [2 marks]

b. Estimate the amount of removed particles when the daily rainfall is 4.8 units.

[1 mark]

c. Determine if daily rainfall influences the amount of removed particles in a linear

relationship. Test at = 0.05. [5 marks]

d. Find the Pearson product moment correlation coefficient for the data set.

Comment your result. [2 marks]

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12. a. In an investigation to determine whether heavy traffic occurring at a particular

segment of highway was random or not, the following data were gathered for

18 days:

+ +

+ ++ + + +

+ +

+ +

where + indicates that the heavy traffic for that day is above average and

- indicates that the heavy traffic for that day is below average. Is the heavy

traffic a random event at significance level = 0.05? [6 marks]

b. The following data give the average flight delay per route (in minutes) for ten

routes before and after deregulation.

Before 10 11 3 5 1 2 11 6 17 18

After 13 12 8 9 8 4 5 14 6 3

Use Wilcoxon signed-rank test, to investigate if there is any difference in flight

delay after deregulation at = 0.05. [6 marks]

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Engineering Statistics SSE2193_Final_Sem1_0607

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