Formulating Hypotheses& Errors in testing of

hypothesis Business Research Methodology

MBA : 2nd Semester

Presented by :

Shantayya.S.G

Basic Concepts in Hypotheses Testing Meaning of Hypothesis TestingNull Hypotheses & Alternate HypothesesType I & Type II ErrorsOne Tailed & Two Tailed TestSteps in formulating Hypotheses Testing

What is Hypothesis testingHypothesis is the making an assumption about the

population parameter. OR

A set of logical and statistical guidelines used to make decisions from sample statistics to population characteristics.

For example: The customer loyalty of brand A is better than brand B.

Null Hypothesis(Ho): The null hypothesis (H0) refers to a hypothesized

testing numerical value or range of values of the population parameter.

Specific statement about a population parameter made for the purposes of argument.

States the assumption to be tested, is a status quo.

Is always about a population parameter, not about a sample statistic.

Example of Ho:In a clinical trial of a new drug, the null

hypothesis might be that the new drug is no better, on average, than the current drug. We would write

H0: there is no difference between the two drugs on an average.

Alternate Hypothesis(HA)An alternatives hypothesis (H1) is the logical

opposite of the null hypothesis.

Represents all other possible parameter values except that stated in the null hypothesis.

Challenges the status quo.

Hypothesis that is believed (or needs to be supported) by the researcher –a research hypothesis.

Example of HA In the clinical trial of a new drug, the alternative

hypothesis might be that the new drug has a different effect, on average, compared to that of the current drug. We would write

HA: the two drugs have different effects, on average. or

HA: the new drug is better than the current drug, on average.

The result of a hypothesis test:

‘Reject H0 in favour of HA’ OR ‘Do not reject H0’

Type I Error: If the null hypothesis is true and we reject it is

called type I error.

Rejected H0 because the results occurred by chance

Conclude that there is a significant effect, even though no true effect exists

Probabilities of Type 1 error called – alpha (a)Determined in advance, typically 5%

Type II Error: If the null hypothesis is false and we accept it

is called type II error.Accept H0 even though it is not trueConclude that there is no significant effect,

even though a true difference existsProbabilities of Type II error called – beta (b)

Type I Error & Type II Error

Accept H0 Reject H0

Correct Decision Type I Error

Type II Error Correct Decision

Ho (True)

Ho (False)

One Tail Test: Rejection of null hypothesis for significant

deviation from the specified value Ho in one direction (tail) of the curve of sampling distribution is called one tailed test.

For example: Boll pen better then ink pen .

Two Tailed Test: Rejection of null hypothesis for significant

deviation from the specified value Ho in both the direction (tail) of the curve of sampling distribution is called two tailed test.

Foe example: A product is manufactured by a semi-

automatic machine. Now, assume that the same product is manufactured by the fully automatic machine. This will be two-sided test, because the null hypothesis is that “the two methods used for manufacturing the product do not differ significantly.

Steps in Hypotheses Testing

1. Formulation of the null and alternate hypothesis

2. Definition of a test statistic3. Determination of the distribution of the test

statistic4. Definition of critical region of the test statistic5. Testing whether the calculated value of the

test statistic falls within the acceptance region.

1: Formulation of H0The Null hypothesis assumes a certain

specific value for the unknown population parameter.

Defined as an inequality – greater than or less than.

For example, if the mean of a population is considered, then

H0: μ ≤ μ0

H0: μ = μ0

H0: μ ≥ μ0

2: Formulation of HaThe alternate hypothesis assigns the values

to the population parameter that is not contained in the null hypothesis.

For example,Ha: μ > μ0

Ha: μ ≠ μ0

Ha: μ < μ0

The null hypothesis is accepted or rejected on the basis of the information provided by the sample.

3: Definition of a Test StatisticA test statistic must be defined to test the

validity of the hypothesis.

The test statistic is computed from sample information.

A number calculated to represent the match between a set of data and the expectation under the null hypothesis

4: Determination of the distribution of the test statistic

The probability distribution of the test statistic depends on the null hypothesis assumed, the parameter to be tested, and the sample size. Commonly used ones are the Normal, “t”, Chi-square and F-distributions.

5: Definition of the critical region for the test statisticThe set of values of the test statistic that

leads to the rejection of H0 in favour of Ha is called the rejection region or critical region.

Depends upon whether the testing is one-sided or two-sided.

6: Decision ruleA decision rule is used to accept or reject the null

hypothesis.

P- valueP < αReject the null hypothesisStatistically significant

Test statisticTest statistic (calculated value) < Table value of αAccept H0

Statistically insignificant

Thank you