EQT 373 Statistics for Engineers

UNIVERSITI MALAYSIA PERLIS

TEST 1

09 February 2011

EQT 373 – Statistics for Engineers

Time: 1 Hour and 30 Minutes

INSTRUCTIONS

Please make sure that this question booklet has FOUR (4) printed pages including the front page.

This question booklet has THREE questions. Answer ALL questions.

You are required to answer all the questions in this question booklet.

All necessary working must be shown clearly.

NAME: ______

MATRIC NUMBER: ______

GROUP / COURSE: ______

LECTURER: ______

Question 1:

The breaking strength X of a certain rivet used in a machine engine has normally distributed with a mean 5000 psi and standard deviation 400 psi. A random sample of 36 rivets is taken.

(i)What is the probability that the sample mean falls between 4800 psi and 5200 psi? (5 Marks)

(ii) What sample nof rivets would be necessary in order to have the probability for sample mean between 4900 and 5100 is 0.99?

(5 Marks)

Solution

Question 2:

A scientist interested to know whether there is a difference in the average daily intakes of dairy product between men and women. He took a sample of adult women and recorded their daily intakes of dairy products in grams per day. He did the same for adult men. A summary of his sample results is listed in table below:

Men / Women
Sample size / 50 / 50
Sample mean / 756 / 762
Sample standard deviation / 35 / 30

(i)Construct a 95% confidence interval for the difference in the average daily intakes of dairy products for men and women.

(4 Marks)

(ii)Can you conclude that there is a difference in the average daily intakes for men and women? Test the hypothesis using .

(6 Marks)

Solution
95% CI for the difference in the average daily intakes of dairy products for men and women:

The hypothesis to be tested are:

Rejection region: or .

Therefore, test statistic is:

Since -0.9204 does not less than -1.96and also not exceed than1.96, we fail to reject (accept ) and that is, there is not sufficient evidence to declare that there is a difference in the average daily intakes of dairy products for men and women:

Question 3:

A Human Resource manager of a large firm believes there may be a relationship between absenteeism and age of workers. A random sample of 10 workers were chosen and the results below were obtained.

Age (years), x / Day absent in a year, y
27 / 15
61 / 6
37 / 10
23 / 18
46 / 9
58 / 7
29
36
64
40 / 14
11
5
8

(i)Find the regression line of day absent in a year (Y) on age (X).

Given:

;;; ;

(7 Marks)

(ii)Predict how many days a 45 year-old worker would be absent from work.

(2 Marks)

(iii)Interpret the meaning of value in part (i).

(1 Marks)

Solution
i)





The regression model is
ii)

iii)
. This means if age increase by one year, the number of days absent would decrease by o.27 days.

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LIST OF FORMULAS

Binomial distribution

,

Normal distribution

,

Sampling distributions

Confidence interval

, is known

, is unknown,

, is unknown,

. where

Hypothesis testing:

For :

For 1 - 2:

Where

For P:

and

For P1 -P2 :

and

Simple Linear Regression

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