Following points are presented in this presentation. 1. Hypothesis testing is a decision-making process for evaluating claims about a population. 2. NULL HYPOTHESIS & ALTERNATIVE HYPOTHESIS. 3. Types of errors.

1. TESTING OF HYPOTHESIS
PRESENTED BY
Swati Singh - 53

2. DEFINITION OF HYPOTHESIS
Hypothesis testing is a decision-making process for evaluating claims
about a population.
Hypothesis testing is an act in statistics whereby an analyst tests an
assumption regarding a population parameter. The methodology employed
by the analyst depends on the nature of the data used and the reason for
the analysis. Hypothesis testing is used to infer the result of a hypothesis
performed on sample data from a larger population.
E.g. the hospital administrator may want to test the hypothesis that the
average length of stay of patients admitted to the hospital is 5 days.

3. DEFINITION OF STATISTICAL HYPOTHESIS
TESTING
It is a conjecture about a population parameter. This conjecture may or
may not be true.
They are hypothesis that are stated in such a way that they may be
evaluated by appropriate statistical techniques.
There are two hypotheses involved in hypothesis testing
• Null hypothesis
• Alternative hypothesis

4. NULL HYPOTHESIS
&
ALTERNATIVE HYPOTHSIS

5. NULL HYPOTHESIS
• Null Hypothesis is the hypothesis which
is tested for possible rejection under the
assumption that is true.
• It is denoted by H0.
• H0 may usually be considered the
skeptic’s hypothesis Nothing new or
interesting happening here. (And
anything “interesting” observed is due to
chance alone.)
• H0 is always stated as an equality claim
involving parameters.

6. ALTERNATIVE HYPOTHSIS
• Any hypothesis which is
complementary to the null
hypothesis is called an
alterative hypothesis. It is
usually denoted by H1.
• The acceptance or rejection of
H is meaningful only if it is
being tested against a rival
hypothesis.
• Ha is an inequality claim that
contradicts H0. It may be one-
sided (using either > or <) or
two-sided (using ≠).

7. IMPORTANCE OF HYPOTHESIS
• Hypothesis forces us to think
more deeply about the
possible outcomes of a study.
• It prevents blind research.
• It formulates clear & specific
goals.
• It links related facts.

8. Types of Errors in Testing of
Hypothesis

9. The table summarizes the four possible outcomes for a
hypothesis test.
Test Rejects
Null
Test Fails to
Reject Null
Null is True
Type I Error
False Positive
Correct decision
No effect
Null is False
Correct decision
Effect exists
Type II error
False negative

10. GRAPHING TYPE I AND TYPE II ERRORS
 The critical region line represents the point at
which you reject or fail to reject the null
hypothesis.
 The distribution on the left represents the null
hypothesis. If the null hypothesis is true, you
only need to worry about Type I errors, which is
the shaded portion of the null hypothesis
distribution. The rest of the null distribution
represents the correct decision of failing to
reject the null.
 On the other hand, if the alternative hypothesis
is true, you need to worry about Type II errors.
The shaded region on the alternative hypothesis
distribution represents the Type II error rate. The
rest of the alternative distribution represents the
probability of correctly detecting an effect—
power.

11.  Moving the critical value line is equivalent to changing the significance level. If you move the line to the
left, you’re increasing the significance level (e.g., α 0.05 to 0.10). Holding everything else constant, this
adjustment increases the Type I error rate while reducing the Type II error rate. Moving the line to the right
reduces the significance level (e.g., α 0.05 to 0.01), which decreases the Type I error rate but increases the
type II error rate.
NOTE: A significance level, also known
as alpha or α, is an evidentiary standard
that a researcher sets before the study. It
defines how strongly the sample evidence
must contradict the null hypothesis before
you can reject the null hypothesis.
In other words, it is the probability that
you say there is an effect when there is no
effect.
For instance, a significance level of 0.05
signifies a 5% risk of deciding that an
effect exists when it does not exist.

12. ONE TAILED
AND
TWO TAILED TESTS

13. ONE TAILED TEST
• A hypothesis Test in which population parameter is known to fall either left or right
of centre of the sampling distribution is called one tailed test.

14. TWO TAILED TEST
• A statistical test in which critical area of a distribution is two sided and tests
whether a sample is greater than or less than a certain range of values.

15. EXAMPLE

16. HYPOTHESIS TESTING
PROCEDURE

17. • We can use any one of the following two methods.
1. Rejection region method
• Null hypothesis
• Alternative hypothesis
2. P-Value estimation method.

18. Null hypothesis
• Step 1: state the null hypothesis.
The null hypothesis can be thought of as the opposite of the "guess" the research
made.
For ex. If the question would be are teens better at maths than adults? Then null
hypothesis will state that AGE HAS NO EFFECT ON MATHEMATICAL
ABILITY. The null hypothesis is always denoted by H0.
Step 2: state the alternative hypothesis.
It is contrary to the null hypothesis.
• The reason we state the alternative hypothesis this way is that if the Null is
rejected, there are many possibilities.
• For example if our null is that I am going to win up to 7 medals then our
alternate is I am going to win more than 7 medals.
• The alternate hypothesis is always denoted by H1.

19. Step 3: level of significance
• Choose the appropriate level of significance(𝛼) depending on the permissible
risk. α is fixed in advance before drawing of the sample.
Step 4: Identifying the sample statistic to be used and its sampling distribution.
Step 5: Test statistic
• Define and compute test statistic under H0.
Step 6: Obtaining the critical value and critical rejections.
Step 7: If the computed value of test statistics lies outside the rejection region we
fail to reject H0. if the computed value of test statistic lies in the rejection region
we reject H0 at level of significance ‘α’.
Step 8: Write the conclusion test in simple language.

20. P- Value estimation method.
In this method most of the steps are similar.
( step 1 to step 5 are similar like rejection region
method).
Step 6: Finding the p-value of the computed test
statistics under H0.
Step 7: If p-value < α, we reject H0 at α level of
significance.
If p-value > α, we fail to reject H0 at ‘α’ level of
significance.
Step 8: write conclusion of the test in simple
language.

21. THANK YOU