A statistical decision in a hypotheses testing problem is either of rejecting or not rejecting H0 based on a given random sample.

**ERRORS IN STATISTICAL HYPOTHESES TESTING**

A **statistical decision** in a hypotheses testing problem is either of
rejecting or not rejecting *H _{0} *based on a given random sample.
Statistical decisions are governed by certain rules, developed

The null hypothesis may be either true or false, in reality. Under
this circumstance, there will arise four possible situations in each hypotheses
testing or decision making problem as displayed in Table 1.5.

It must be recognized that the final decision of rejecting *H _{0}*
or not rejecting

A soft drink manufacturing company makes a new kind of soft drink.
Daily sales of the new soft drink, in a city, is assumed to be distributed with
mean sales of ₹40,000 and standard deviation of ₹2,500 per day. The Advertising
Manager of the company considers placing advertisements in local TV Channels.
He does this on 10 random days and tests to see whether or not sales has
increased. Formulate suitable null and alternative hypotheses. What would be
type I and type II errors?

The Advertising Manager is testing whether or not sales increased
more than ₹40,000.

Let μ be the average amount of sales, if the advertisement does
appear.

The null and alternative hypotheses can be framed based on the
given information as follows:

**Null hypothesis: ***H*_{o}:** ***μ*** **= 40000

*i.e*., The mean sales due to the advertisement is not significantly
different from ₹40,000.

**Alternative hypothesis: ***H*_{1}:** ***μ*** **> 40000

*i.e*., Increase in the mean sales due to the advertisement is
significant.

(i) If type I error occurs, then it will be
concluded as the advertisement has improved sales. But, really it is not.

(ii) If type II error occurs, then it will be concluded that the
advertisement has not improved the sales. But, really, the advertisement has
improved the sales.

The following may be the penalties due to the occurrence of these
errors:

If type I error occurs, then the company may spend towards
advertisement. It may increase the expenditure of the company. On the other
hand, if type II error occurs, then the company will not spend towards
advertisement. It may not improve the sales of the company.

Tags : Definition, Example Solved Problems | Statistics , 12th Statistics : Chapter 1 : Tests of Significance - Basic Concepts and Large Sample Tests

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12th Statistics : Chapter 1 : Tests of Significance - Basic Concepts and Large Sample Tests : Errors in Statistical Hypotheses Testing | Definition, Example Solved Problems | Statistics

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