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
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
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
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
