(ASSIGNMENT TEMPLATE – ENGLISH VERSION) (COVER PAGE)

FACULTY SCIENCE AND TECHNOLOGY

SEMESTER JANUARY / 2015

SBST2103

SAMPLING DISTRIBUTION AND HYPOTHESIS TESTING

MATRICULATION NO : 820901035758002

IDENTITY CARD NO. : 820901035758

TELEPHONE NO. : 010-9086024

E-MAIL : saneeya@oum.edu.my

LEARNING CENTRE : PPK

SBST2103 SAMPLING DISTRIBUTION AND HYPOTHESIS TESTING

Table of content

Question 1 page

(a) 2

(b) 3

(c) 4

(d) 5

Question 2

(a) 6

(b) 7-8

Question 3 9-10

Question 4 11-13

References 14

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SBST2103 SAMPLING DISTRIBUTION AND HYPOTHESIS TESTING

QUESTION 1

, given

a) Between 1000 and 1250 hours

Answer:

2

SBST2103 SAMPLING DISTRIBUTION AND HYPOTHESIS TESTING

b) More than 1250 hours

Answer:

3

SBST2103 SAMPLING DISTRIBUTION AND HYPOTHESIS TESTING

c) Between 901 and 1000 hours

Answer:

4

SBST2103 SAMPLING DISTRIBUTION AND HYPOTHESIS TESTING

d) Between 901 and 1250 hours

Answer:

5

SBST2103 SAMPLING DISTRIBUTION AND HYPOTHESIS TESTING

QUESTION 2

Given

a) If the sample mean is chosen as a point estimator for the population mean .

Determine whether is an unbiased estimator for .

Solution:

is chosen as a point estimator for population mean, .

As we know that ;

An estimator is unbiased if .

Therefore,

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SBST2103 SAMPLING DISTRIBUTION AND HYPOTHESIS TESTING

Answer: is an unbiased estimator for .

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SBST2103 SAMPLING DISTRIBUTION AND HYPOTHESIS TESTING

b) Determine the sampling distribution for the sample mean, and calculate the

mean and the standard deviation for .

Solution:

Population distribution

Shape : normal

Mean,

Standard deviation,

The sampling distribution of sample mean,

Small sample size :

Shape:normal

The claim that population is RM1800. The population mean is used to

verify the claim. The sample mean is equal to population mean .

Thus, it is more appropriate to defend the statement that or restate

that ? From the case II above, the standard score is given by:

with degree of freedom.

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SBST2103 SAMPLING DISTRIBUTION AND HYPOTHESIS TESTING

Hence, .

From t- table, with 19 degree of freedom, we obtain

If , then is less than 1.729

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SBST2103 SAMPLING DISTRIBUTION AND HYPOTHESIS TESTING

QUESTION 3

Given

Solution:

Since p is unknown; so the point estimator for the parameter p is:

99% confidence interval for the true proportion of smokers who believe that smoking

should be banned from public buildings.

Thus,

The distribution for approaches normal with mean. So, from the standard normal table,

we get:

(from table)

A random sample of size is chosen from a population where is unknown and is

used as an estimator of . Then, the estimate of confidence interval for

is:

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SBST2103 SAMPLING DISTRIBUTION AND HYPOTHESIS TESTING

It means that we are 99% confident that the true proportion of smokers who believe that

smoking should be banned from public buildings is between 26% and 36%.

As we know that .

Then, by using Theorem 2.5 (page 40), the sample size necessary to reduce the maximum

error to 0.03 with a 99% confidence is:

Hence, the estimate based on the sample size, with a 99% confidence that the

sample proportion of smokers who believe that smoking should be banned from public

buildings, will differ from the true proportion by less than or not more than 0.03 .

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SBST2103 SAMPLING DISTRIBUTION AND HYPOTHESIS TESTING

QUESTION 4

Type II Error means that in hypothesis testing an error incurred by Failing to reject or

Not rejecting or Accept the null hypothesis when is actually FALSE. Therefore,

the probability type II error is denoted by . and then

.

The power of test means that the probability of rejecting the null hypothesis when it

is False. The power is to measure the sensitivity of the test to detect a real difference in

parameters if it is exists.

FAIL TO REJECT the hypothesis null if

That means reject when

, Given

Hypothesis formulation:

(claim)

Type of test : two-tailed test

If is actually equal to 870 ;

The power of the test is:

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SBST2103 SAMPLING DISTRIBUTION AND HYPOTHESIS TESTING

....LHS

(from table)

....RHS

Thus, from table for

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SBST2103 SAMPLING DISTRIBUTION AND HYPOTHESIS TESTING

;

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SBST2103 SAMPLING DISTRIBUTION AND HYPOTHESIS TESTING

REFERENCES

1. Prof Dr Mohd Kidin Shahran & et.al, August 2013, SBST2103 Sampling

Distribution and Hypothesis Testing, Open University Malaysia, Meteor Doc Sdn

Bhd, Selangor Darul Ehsan.

2. Allan G. Bluman, Elementary Statistics: A Step By Step Approach, Fifth Edition,

Mc Graw Hill, Mc Graw Hill Companies, Avenue of Americas, New York.

3. Mario F. Triola, Elementary Statistics, 11th Edition, Addison-Wesley, Pearson,

United States of America.

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