This document discusses hypotheses, including their characteristics, criteria for construction, testing approaches, and types of errors. It defines a hypothesis as a tentative explanation for behaviors or events that can be scientifically tested. Key points include: - Hypotheses must be clear, precise, testable and specify the relationship between variables. - The null hypothesis is what is being tested, while the alternative is what may be accepted if the null is rejected. - Tests can be two-tailed, testing in both directions, or one-tailed, testing in one specified direction. - Type I error occurs when a true null hypothesis is rejected, while Type II error is accepting a false null hypothesis.

1. Bidyadhar (04)
Manoj (13)
Rashmi (14)
Sunil (15)
Yash (16)
Asha (19)

2.  INTRODUCTION
 CHARACTERISTICS OF A HYPOTHESIS
 CRITERIA FOR HYPOTHESIS CONSTRUCTION
 STEPS IN HYPOTHESIS TESTING
 SOURCES OF HYPOTHESIS
 APPROCHES TO HYPOTHESIS TESTING
 THE LOGIC OF HYPOTHESIS TESTING
 TYPES OF ERRORS IN HYPOTHESIS

3. “Don’t confuse “hypothesis” and “theory”. The
former is a possible explanation; the latter, the
correct one. The establishment of theory is the very
purpose of science.”
- Martin H. Fischer
 A Hypothesis is :-
 a mere assumption to be proved or disproved
 the statement or an assumption about relationships
between variables
 a tentative explanation for certain behaviors,
phenomenon or events that have occurred or will occur
 a predictive statement capable of being tested by scientific
methods, that relates an independent variable to some
dependent variable

4.  Hypothesis is a principal instrument in
research and for researcher its a formal question
that he intends to resolve
 Most research is carried out with the deliberate
intention of testing hypothesis
 Decision makers need to test hypothesis to take
decisions regarding alternate courses of action
 Hypothesis-testing, thus, enables us to make
probability statements about population
parameters
 In sum, hypothesis is a proposition which can
be put to test to determine its validity

5.  Students who receive counseling will show
greater increase in creativity than students not
receiving counseling; or Car A is performing as
well as Car B
 Bankers assumed high-income earners are
more profitable than low-income earners.
 Old clients were more likely to diminish CD
balances by large amounts compared to
younger clients.
This was nonintrusive because conventional
wisdom suggested that older clients have a
larger portfolio of assets and seek less risky
investments

6. o Should be clear and precise
o Should be capable of being tested
o Should be limited in scope and be specific
o Should be stated in simple terms
o Should state the relationship between variables
o Should be consistent with most known facts
o Should be amenable to testing within a reasonable time
o Must explain the facts that gave rise to the need for
explanation

7.  It should be empirically testable, whether it is
right or wrong.
 It should be specific and precise.
 The statements in the hypothesis should not be
contradictory.
 It should specify variables between which the
relationship is to be established.
 It should describe one issue only.

9.  Theory
 Main source
 Observation
 Through observing the environment
 Analogies
 Intuition & personal experience

10.  Classical statistics
 Represents an objectives view of probability in which the
decision making rests totally on an analysis of available
sampling data
 A hypothesis established, it is rejected or accepted, based
on the sample data collected
 Bayesian statistics
 Its extension of classical approach
 But goes beyond to consider all other available
information
 This additional information consist of subjective
probability estimates states in terms of degrees of belief
 Subjective estimates are based on general experience
rather than on specific collected data

11.  In classical tests of significance, two kinds of
hypothesis are used
 Null hypothesis
 Alternative hypothesis
 Two-tailed test
 One-tailed test

12.  Null hypothesis (H0) represents the hypothesis we are
trying to reject and is the one which we wish to disprove
: 0  0 0     New Std New Std H    
 Example:
1) Suppose a coin is suspected of being biased in favor
of heads. The coin is flipped 100 times & the outcome is
52 heads. It would not to be correct to jump to the
conclusion that the coin is biased simply because more
than the expected number of 50 heads resulted. The
reason is that 52 heads is consistent with the
hypothesis that the coin is fair. On the other hand,
flipping 85/90 heads in 100 flips would seem to
contradict the hypothesis of a fair coin. In this case
there would be a strong case for a biased coin.

13.  Given the test scores of two random samples of
men and women, does one group differ from the
other? A possible null hypothesis is that the mean
male score is the same as the mean female score:
H0: μ1 = μ2where:
H0 = the null hypothesis
μ1 = the mean of population 1, and
μ2 = the mean of population 2.
A stronger null hypothesis is that the two samples
are drawn from the same population, such that the
variance and shape of the distributions are also
equal.

14. • Alternative Hypothesis (Ha or H1) is usually
the one which we wish to prove and the
alternative hypothesis represents all other
possibilities.
:   0 A New Std H  
• Further, alternative hypothesis it has two
types are:
•Two-tailed test
•One-tailed test

15.  It is non-directional test which considers two possibilities
 If you are using a significance level of 0.05, a two-tailed test
allots half of your alpha to testing the statistical significance
in one direction and half of your alpha to testing statistical
significance in the other direction.
 This means that .025 is in each tail of the distribution of your
test statistic.
 When using a two-tailed test, regardless of the direction of
the relationship you hypothesize, you are testing for the
possibility of the relationship in both directions.
 Example, we may wish to compare the mean of a sample to
a given value x using a t-test. Our null hypothesis is that the
mean is equal to x. A two-tailed test will test both if the
mean is significantly greater than x and if the mean
significantly less than x. The mean is considered
significantly different from x if the test statistic is in the top
2.5% or bottom 2.5% of its probability distribution, resulting
in a p-value less than 0.05.

17.  It is unidirectional test
 If you are using a significance level of .05, a one-tailed test allots all of
your alpha to testing the statistical significance in the one direction of
interest.
 This means that .05 is in one tail of the distribution of your test statistic.
 When using a one-tailed test, you are testing for the possibility of the
relationship in one direction and completely disregarding the possibility
of a relationship in the other direction.
 Let's return to our example comparing the mean of a sample to a given
value x using a t-test.
 Our null hypothesis is that the mean is equal to x. A one-tailed test will
test either if the mean is significantly greater than x or if the mean is
significantly less than x, but not both. Then, depending on the chosen tail,
the mean is significantly greater than or less than x if the test statistic is in
the top 5% of its probability distribution or bottom 5% of its probability
distribution, resulting in a p-value less than 0.05. The one-tailed test
provides more power to detect an effect in one direction by not testing the
effect in the other direction. A discussion of when this is an appropriate
option follows.

19. Types of errors Types of errors
Types of decision H0true H0 false
Reject Type I error(a) Correct decision(1-b)
Accept Correct decision(1-a) Type II error(b)

20.  Type I Error – we may reject the null
hypothesis when it is true;
 That is, Type I error means rejection of the
hypothesis which should have been accepted
 The value is called level of significance and
probability of rejecting the true
 Example: the innocent person is unjustly
convicted

21.  Type II Error – we may accept the null
hypothesis when in fact the null hypothesis is
not true
 Type II error means accepting the hypothesis
which should have been rejected
 Example: the result is an unjust acquittal, with
the guilty person may go free