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WHAT IS A HYPOTHESIS

Hypothesis is an unproven proposition or supposition that tentatively explains certain facts or

phenomena.

A hypothesis is a statement , an assumption about the nature of the world

Hypothesis is a guess

With statistical techniques we are able to decide whether or not our theoretical hypotheses areconfirmed by the empirical evidence

NULL AND ALTERNATIVE HYPOTHESIS

Null hypothesis:

Conservative statement that communicates the notion that any change from what hasbeen thought to be true or observed in the past will be due entitrely to random error

True purpose of setting null hypothesis is to provide an opportunity to nullify it.

Null hypothesis is a no difference hypothesis

Alternative hypothesis

Alternative hypothesis would be there is difference- i.e it states the opposite of nullhypothesis

The purpose of hypothesis testing is to determine which of the hypothesis is true

PROCEDURE OF HYPOTHESIS TESTING

1. determine statisticsal hypothesis

2. imagine sampling distribution if the hypothesis were true.

3. take actual sample and calculate mean or appropiate statistic

4. We expect some small difference ( although there may be large) between the sample mean andpopulation mean.We then must determine if the deviation between the obtained value of the sample

mean and its expected value ( based on the statistical hypothesis) would have occurred by chance alone

say 5 times out of 100- if the statistical hypothesis were true.5. Statisticians have defined the decision criterion as the significance level.

6. Significance level is a critical probability in choosing between the null hypothesis and the alternative

hypothesis

CONFIDENCE INTERVAl/ LEVEL OF SIGNIFICANCE

It is regarded as the set of acceptable hypothesis or the level of probability associated with an interval

estimate..

In hypothesis testing, statisticians change their terminology and call this the level of significance ( )

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CRITICAL VALUES:

The values that lie exactly on the boundary of the region of rejectionare critical values of .

CRITICAL REGION

The region of acceptance is called critical region

TYPE I and TYPE II ERRORS

Wecannot make statement about the sample with complete certainity, there is always a chance that

error will be made.

Researchers run the risk of committting two types of errors.

DECISION

State of null hypothesis inpopulation

Accept Ho Reject H0

H0 is true

Correct- no error Type I Error ( )

H0 is false Type II error ( )

Correct-no error

In business problems,TypeI errors are generally more serious than type II errors,

There is greater concern with determining the significance level,alpha , than with determining beta.

CHOOSING THE APPROPIATE STATISTICAL TECHNIQUE

Choice of appropiate method of statistical analysis depends on-

1. type of question to be answered

2. the number of variables

3. the scale of measurement

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Z-test Test of significance proportions and test of significance of mean for large

samples. One sample as well as two s amples

t- test Test of significance of mean (means) small samples ( one or two)

If two could be normal or paired

F-test Test of significance of homogeneity of several means ( more than two samplemeans)

Chi-square test Test of significance for proportions ( three or more than three samples

Proportions

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