# Estimation Theory MBA 1st Year Semester Long Question Answer Study Notes

Purpose of Hypothesis Testing

The major purposes of hypothesis testing are as follows: 1. To find out whether the difference in the estimated value of the parameter and the true value, if known, is significant or it could have arisen due to fluctuation of sampling.

2. To find out whether the results given to us by two different samples drawn from the same universe are consistent with each other.

3. To find out whether the differences between their values are insignificant and could not have arisen due to fluctuations of sampling.

In all such cases where we have to find out whether the difference between statistic and parameter, or the difference between two values given by two samples drawn from the same universe are insignificant or whether it could have been on account of sampling fluctuations, we formulate a hypothesis and test its validity.

Procedure for Hypothesis Testing

To test a hypothesis means to tell (on the basis of the data the researcher has collected) whether or not the hypothesis seems to be valid. In hypothesis testing, the main question is: whether to accept the null hypothesis or not to accept the null hypothesis? Procedure for hypothesis testing refers to all those steps that we undertake for making a choice between the two actions, i.e. rejection and acceptance of a null hypothesis. The various steps involved in hypothesis testing are enumerated below:

1. Making a Formal Statement: The step consists in making a formal statement of the null hypothesis (H.) and also of the alternative hypothesis (H1). This means that hypothesis should be clearly stated, considering the nature of the research problem.

(a) Null Hypothesis, Ho: It is of status quo or of no difference and is used to decide whether or not to accept the hypothesis (For example, a population parameter u).

H, u = X Ho u = lo

(b) Alternate Hypothesis, H : It is opposite of null hypothesis.

Hu 34, (ie.u>H, oru<ue)

Hence, H, and H, both can’t be true.

The formulation of hypothesis is an important step which must be accomplished with due care in accordance with the object and nature of the problem under consideration. It also indicates whether w a ne tailed test or a two tailed test.

Selecting a Significance Level: The hyp sonificance and as such the same should be specified. Generally, in practice, either 5% level or 1% level is adopted for the purpose. The factors that affect the level of significance are:

1 is adopted for the purpose. The factors that affect

(a) The magnitude of the on the difference between sample means.

(b) The size of the samples.

(c) The variability of bility of measurements within samples.

(d) Whether the hypothesis is directional or non-directional.

In brief, the level of significance must be adequate in the context of the purpose and nature of enquiry.

3. Deciding the Distribution to Use: After deciding to ypothesis testing is to determine the appropriate sampling distribution. The choice generally remains similar to those which we have stated earlier in the context of estimation.

4.Selecting a Random Sample and Computing an Appropriate value: Another step is to seier utilising the relevant distribution. In other words, draw a sample to furnish empirical data.

5. Calculation of the Probability: One has then to calculate the probability that probability that the sample result would diverge as widely as it has from expectations, if the null hypothesis were in fact true.

6. Comparing the Probability: Yet another step consists in comparing the probability thus or calculated with the specified value fora, the significance level. If the calculateu p un smaller than the a value in case of one tailed test sanda/2 in case of two tailed test), then reject the null hypothesis (1.e. accept the alternative hypothesis), but if the calculated probability is greater, then accept the null hypothesis. In case we reject H.. we run a risk of (at most the level of significance) committing an error of type I, but if we accept Ho, then we run some risk (the size of which cannot be specified as long as the H, happens to be vague rather than specific) of committing an error of type II.

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