This document discusses hypothesis testing. It defines a hypothesis as a predictive statement that relates independent and dependent variables and can be scientifically tested. The purpose of a hypothesis is to define relationships between variables. Characteristics of a good hypothesis are outlined. Null and alternative hypotheses are defined, with the null being what is currently assumed to be true. Type I and Type II errors in hypothesis testing are explained. Common statistical tests used to test hypotheses are described briefly, including t-tests, z-tests, F-tests, and chi-square tests. Key concepts like significance levels, confidence intervals, and contingency tables are also summarized.

1. Hypothesis
Testing

2. Prepared For :
Md. Mahedi Hasan
Lecturer, Statistics
Bangladesh University
of Professionals

3. The Mayanchu
Squad
Prepared By:
Group Members:
Riffat Afrin Maisha (B1405066)
Tasnia Ahmed (B1405072)
Shafat Bin Farid Shefa(B1405129)
Shahabul Hossain (B1405132)
Momo Dewan (B1405156)
Rabiul Alam (B1405159)

4. What is Hypothesis?
 Hypothesis is a predictive statement,
capable of being tested by scientific
methods, that relates an independent
variables to some dependent variable.
 A hypothesis states what we are looking
for and it is a proportion which can be put
to a test to determine its validity

5. PURPOSE OF HYPOTHESIS
 Defining relationship between variables
 Variable- changing quantities in a study
 Independent variable
 Dependent variable
 Controlled variable

6. Characteristics of Hypothesis
 Clear and precise.
 Capable of being tested.
 Stated relationship between variables.
 limited in scope and must be specific.
 Consistent with most known facts.

7. Characteristics of Hypothesis
 Responsive to testing with in a reasonable time.
One can’t spend a
life time collecting data to test it.
 Explain what it claims to explain; it should have
empirical reference.
 Stated as far as possible in most simple terms so
that the same is
easily understand by all concerned. But one must
remember that
simplicity of hypothesis has nothing to do with its
significance.

8. Null Hypothesis
 It is an assertion that we hold as true unless
we have
sufficient statistical evidence to conclude
otherwise.
 Null Hypothesis is denoted by 𝐻0
 If a population mean is equal to
hypothesized mean then Null Hypothesis
can be written as
𝐻0: 𝜇 = 𝜇0

9. Null Hypothesis (H0)
 Alternative Hypothesis (Ha or H1)
Each of the following statements is an
example of a null hypothesis and alternative
hypothesis.
𝐻0: 𝜇 = 𝜇0
𝐻0: 𝜇 ≤ 𝜇0
𝐻0: 𝜇  𝜇0
𝐻a: 𝜇 ≠ 𝜇0
𝐻a: 𝜇 > 𝜇0
𝐻a: 𝜇 < 𝜇0

10. Alternative Hypothesis
 The Alternative hypothesis is negation of
null hypothesis and is denoted by 𝐻 𝑎
If Null is given as 𝐻 0: 𝜇 = 𝜇0
Then alternative Hypothesis can be
written as :
𝐻 𝑎: 𝜇 ≠ 𝜇0
𝐻 𝑎: 𝜇 > 𝜇0
𝐻 𝑎: 𝜇 < 𝜇0

11. Level of significance and
confidence
 Significance means the percentage risk to reject
a null hypothesis when it is true and it is denoted
by 𝛼. Generally taken as 1%, 5%, 10%
 (1 − 𝛼) is the confidence interval in which the null
hypothesis will exist when it is true.

12. Type I and Type II Error
1. Type I Error
– Reality: No relationship
– Decision: Reject the null
• Believe your research hypothesis have
received support when in fact you should
have disconfirmed it
• Analogy: Find an innocent man guilty of a
crime

13. Type I and Type II Error
2. Type II Error
Reality: Relationship
Decision: Accept the null
Believe your research hypothesis has not
received support when in fact you should
have rejected the null.
Analogy: Find a guilty man innocent of a
crime

14. Type I and Type II Error

15. Methods used to test
hypothesis
 T test
 Z test
 F test
 χ 2 test (Chi-Square Test)

16. T-Test
 A t-test’s statistical significance indicates whether
or not the difference between two groups’
averages most likely reflects a “real” difference in
the population from which the groups were
sampled.

17. T-Test for testing difference
between means
Test Condition
 Samples happen to be small,
 Presumed to have been
drawn from the same
population
 Population variances are
unknown but assumed to be
equal
Test Statistics

18. Graph : T Test

19. Z-Test
Test Condition
 Populations are normal
 Samples happen to be large
 Presumed to have been
drawn from the same
population
 Population variances are
known
Test Statistics

20. F-Test
• F-test is a statistical test that is used to
determine whether two populations having
normal distribution have the same variances
or standard deviation. This is an important
part of Analysis of Variance (ANOVA).
However in case the population is non
normal, F test may not be used and
alternate tests like Bartlett’s test may be
used.

21. Chi square (χ2 ) test
The test we use to measure the differences
between what is observed and what is
expected according to an assumed
hypothesis is called the chi-square test.

22. Usefulness
 Test for goodness of fit
 Test for independence of attributes
 Testing homogeneity
 Testing given population variance

23. Contingency table
Frequency table in which a sample from a
population is classified according to two
attributes, which are divided in to two or more
classes
DRUNKARDS NON
DRUNKARDS
GENDER
MALES
675 987
FEMALES
540 997

24. Degrees of Freedom
Number of independent observations
Number of cells – no. of constraints

25. Formula
χ 2 = ∑ (O – E)2
E
χ2 = The value of chi square
O = The observed value
E = The expected value
∑ (O – E)2 = all the values of (O –
E) squared then added together

26. Thank You For Your Patience