Ppt on Statistics fo Business II chapter three

1. CHAPTER THREE:- HYPOTHESIS TESTING
What is hypothesis?
 A hypothesis is a claim or statement about the value of a single population
characteristic or the values of several population characteristics.
 A test of hypotheses or statistical procedure is a method that uses sample
data to decide between two competing claims (hypotheses) about a
population characteristic.
There are two types of hypothesis:
I. Null hypothesis( H0) and
II. Alternative hypothesis( Ha or H1)

2. Null Hypothesis VS Alternative Hypothesis
Null hypothesis:- is the statement about the population parameter
that is assumed to be true unless there is convincing evidence to the
contrary.
• The null hypothesis is usually labeled H0.
• Always contains the ‘=‘ sign H0: ʹμ0= μ
Alternative hypothesis:- is a statement about the population
parameter that is contradictory to the null hypothesis, and is accepted
as true only if there is convincing evidence in favor of it.
Denoted by (Ha) or( H1)
H1 always contradict the H0.
Never contains the’=‘ sign H1:ʹμ0 ≠ μ

3. • In carrying out a test of H0 versus Ha, the hypothesis H0 will be
rejected in favor of Ha only if sample evidence strongly suggests that
H0 is false.
• If the sample does not provide such evidence, H0 will not be
rejected. The two possible conclusions are then reject H0 or fail to
reject H0.

4. Example:-1
• A publisher of college textbooks claims that the average price of all
hardbound college textbooks is 200 Birr A student group believes that
the actual mean is higher and wishes to test their belief. State the
relevant null and alternative hypotheses.
Solution
• The default option is to accept the publisher’s claim unless there is
compelling evidence to the contrary. Thus the null hypothesis is
H0: μ= 200
Since the student group thinks that the average textbook price is
greater than the publisher’s figure, the alternative hypothesis in this
situation is H1: μ > 200

5. Example -2
• The recipe for a bakery item is designed to result in a product that contains
grams of fat per serving. The quality control department samples the
product periodically to insure that the production process is working as
designed. State the relevant null and alternative hypotheses.
Solution
• The default option is to assume that the product contains the amount of
fat it was formulated to contain unless there is compelling evidence to the
contrary. Thus the null hypothesis is H0: μ= 8
• Since to contain either more fat than desired or to contain less fat than
desired are both an indication of a faulty production process, the
alternative hypothesis in this situation is that the mean is different from ,
so H1: μ ≠ 8

6. ERROR IN HYPOTHESIS TESTING
1. Type I error.
• If the null hypothesis is true but the sample mean is such that the null
hypothesis is rejected, a Type I error occurs. The probability that such
an error will occur is the α risk.
2. Type II error.
• If the null hypothesis is false but the sample mean is such that the
null hypothesis cannot be rejected, a Type II error occurs. The
probability that such an error will occur is called the β risk

7. • Type I error: the error of rejecting H0 when H0 true.
• Type II error: the error of failing to rejecting H0 when H0
false.

8. • If the alternative involves showing that some value is greater than or less than a
number, there is some value c that separates the null hypothesis rejection region
from the fail to reject region. This value is known as the critical value.

9. • In the context of Example , suppose that it is known that the
population is normally distributed with standard deviation α= 0.15
gram, and suppose that the test of hypotheses versus will be
performed with a sample of size 5 . Construct the rejection region for
the test for the choiceα= 0.10. Explain the decision procedure and
interpret it.
• Solution
• If is true then the sample mean is normally distributed with mean and
standard deviation

11. EXAMPLE:1
• A government report claims that the average temperature on the
planet Venus is at least 300◦ C. You don’t believe this - you think the
average temperature must be lower - so you carry out an experiment
during which you will measure the temperature on Venus at 100
random times, then compute the mean of the measured
temperatures. If the mean temperature is over 20◦ C less than the
report’s claim, then you will declare the report’s claim false.
• Thus, the null hypothesis is H0 : T = 300 and the alterative hypothesis
is Ha : T < 300. The value c = 280 separates the rejection region from
the fail to reject region; that is, if T < 280, the null hypothesis will be
rejected, and if T ≥ 280, then the null hypothesis will not be rejected.

12. • Suppose that the actual temperature on Venus is indeed
300◦ C (or greater), as the report stated. If the sample mean
has T ≥ 280, then the null hypothesis will correctly be
accepted. If the sample mean has T < 280 then the null
hypothesis will incorrectly be rejected; this is a Type I error.
On the other hand, if the actual temperature on Venus is less
than 300◦ C, but the sample mean has T ≥ 280, then the null
hypothesis will incorrectly be accepted; this is a Type II error.
If the sample mean has T < 280, then the null hypothesis will
correctly be rejected.

23. EXAMPLE-2

27. • Refferring to the example -2 .suppose that the researchers
have asked : can we conclude that 𝜇 < 30.
Data: See previous example
Assumption : See previous example
Hypothesis:
H0 :- 𝜇 = 30
Ha :-𝜇 < 30

31. Example-3

33. The end