This document appears to be an assignment for a course on sampling distribution and hypothesis testing. It contains 4 questions with multiple parts that provide examples and solutions to concepts in hypothesis testing, determining sampling distributions, confidence intervals, type I and type II errors, and power of tests. The document includes a table of contents, references section, and is formatted with page numbers and line breaks between questions/parts.

1. (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

2. 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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3. SBST2103 SAMPLING DISTRIBUTION AND HYPOTHESIS TESTING
QUESTION 1
, given
a) Between 1000 and 1250 hours
Answer:
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4. SBST2103 SAMPLING DISTRIBUTION AND HYPOTHESIS TESTING
b) More than 1250 hours
Answer:
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5. SBST2103 SAMPLING DISTRIBUTION AND HYPOTHESIS TESTING
c) Between 901 and 1000 hours
Answer:
5

6. SBST2103 SAMPLING DISTRIBUTION AND HYPOTHESIS TESTING
d) Between 901 and 1250 hours
Answer:
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7. SBST2103 SAMPLING DISTRIBUTION AND HYPOTHESIS TESTING
QUESTION 2
Given
a) If the sample mean is chosen as a point estimator for the population mean µ.
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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8. SBST2103 SAMPLING DISTRIBUTION AND HYPOTHESIS TESTING
Answer: is an unbiased estimator for .
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9. SBST2103 SAMPLING DISTRIBUTION AND HYPOTHESIS TESTING
b) Determine the sampling distribution for the sample mean, X and calculate the
mean and the standard deviation for X .
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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10. 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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11. 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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12. 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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13. 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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14. SBST2103 SAMPLING DISTRIBUTION AND HYPOTHESIS TESTING
....LHS
(from table)
....RHS
Thus, from table for
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15. SBST2103 SAMPLING DISTRIBUTION AND HYPOTHESIS TESTING
;
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16. 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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