Tests of Hypotheses

7/31/2019 Tests of Hypotheses

1/20

[Former Professor of VIT, Vellore (TN) & BU]

Hypo.Testing/ RNS/kiit 1


2/20


3/20

1.Define Research Problem2.Review Literature (Last finding/ theory/ concept)

3.Formulate Hypothesis

4.Design the Research (Sampling design)5.Collection of data(Observations, response variable)

[ Predictor, criterion variables] Ex. - advt., sales

6. Analysis of data (Hypothesis testing etc.)

7. Interpretation & Final report



4/20

Research gap

Additional knowledge

Trying to know something about the unknown

Population vs Sample

Parameter vs Statistic Census vs sampling

Sampling methods & sampling distributions

Sampling error, standard error

Estimation: point & interval



5/20

of consumers of

Marital status of respondents Annual Income of family2. Relevance of malls, like Bigbazar (to the locals);3. Importance of while buying Mobile,

edible oil4. Use of credit cards;5. Attitude (I)/ Preference(O)

(study on fruit juice Vs soft drink)6. Newspaper popularity;

7. Packaging [study onfor

deodorant];8. Selecting a trusted/ dependable Hospital



6/20

The observational method involves human or

mechanical observation of what people actually door what events take place during a buying or

consumption situation.

are repeated-measurement studies, that collectdata over several periods in time.



7/20

is a declaratory statement that is testable. Itis a statement about the population that we wish to

verify on the basis of available sample information.

- It is a provisional answer to the research problem

under study which is tested empirically for its validity.

The hypothesis tested is generally called

and the other, which gives a reversestatement, is called its



8/20

1.

2.

3. 4.



9/20Hypo.Testing/ RNS/kiit 9

Actual/true-State

Reject (H0) Accept (H0)

H0 True Wrong (Type IError)

CorrectDecision

H0 False Correct

Decision

Wrong (Type II

Error)

Action

Decision from Sample

= Producers risk and = Consumers risk, (chances of)


10/20

the probability of type-1 error, is known as thelevel of significance of the test (= size of the CriticalRegion).

Prob.{Accepting H0 / H1 is true}= ,

(1-

) is called the power of the test.- We cant check/ reduce both & simultaneously.The usual practice is to control at a predeterminedlow level and subject to this constraint on wechoose such a test that minimizes (or maximizesthe power function, 1- ). Generally we choose =0.05 or, 0.01 (i.e. 5% or 1%) level of significance.



11/20

In every test, we compute the value

- E( )Z = --------------

S.E.( )

Where , is the statistic;S.E ( ) is the standard error of the statistic .



12/20Hypo.Testing/ RNS/kiit 12

Large Sample Test


13/20

1. Construct hypotheses (null & Alternative) 2. Select appropriate test statistic (formula)

3. Calculation (calculated value of t or z)

4. Comparison (with tabulated value)

Note: Testtype (one/ two tailed test) depends onH1one/ two tailed test : (z=2.58 or 1.96), for 1% or 5%

one tailed test : (z= 2.33 or 1.645), for 1% or 5%



14/20


n

XZ

/

0

FORMULAE FOR TESTS

Cases: - Large sample test

1. Testing of Mean of a Normal Distribution With Known S. D. ( ):

2. Testing of mean of a Normal Distribution with unknown S.D. ():

Where,

(S is called sample Standard Deviation)

21

1 XX

nS i

nS

Xt

/

0


15/20


,11

21

21

nnS

XXt

2

11

21

2

2212

12

nn

SnSnS

3 (a):Test ofequality of two means with known variances:

(Ho: 1

= 2

)

3(b): Test ofequality of two means where variances are not

known:

,

2

12

1

12

21

nn

XXZ

Where,


16/20


npq

PPZ

/

1

2

22

1

11

21

n

qP

n

qP

PPZ

4 (a): Test of proportions (single sample):

4(b): Test of equality of proportions of two samples:


17/20

t - test when :

(i) Sample size is within 30-40, or less(ii) Population variance or standard deviation isunknown.

While testing hypothesis following are

usually made:(a) the population is normal (or ApproximatelyNormal),(b) Observations are independently drawn for therandom sample.

(c) In case of 2 samples, population variances areequal(for the test of equality of Means)



18/20

This test is used for:

(i) test of dependence or association between

2 attributes,

(ii) test of goodness of fit,

(iii) test of homogeneity (of distributions,correlation coefficients & population variances).

n (Oi- Ei)2

2 ( )= --------

i=1 Ei



19/20


Critical region (or the rejection area)

Accept

Right-tail

Left-tail


20/20


Date post:	05-Apr-2018
Category:	Documents
Upload:	rajivaaf28
View:	221 times
Download:	0 times

Tests of Hypotheses

Documents