Business Statistics Topic Hypothesis testing Class BBA II

Business Statistics Topic: Hypothesis testing Class: BBA II (SEM IV) COLLEGE : I. B. (P. G) COLLEGE, PANIPAT AFFILIATED TO KUK

Introduction: In many circumstances, we are to make decisions about the population on the basis of only sample information. For example, on the basis of sample data, a drug chemist is to decide whether a new drug is really effective in curing the disease. The theory of testing of hypothesis employs various techniques to arrive at such decision basis of sample study Basic Concept of hypothesis testing Hypothesis: in attempt to arrive at decisions, it is necessary to make assumptions about population parameters involved such assumptions is called statistical hypothesis which may or may not be true. There are two types of hypothesis • Null hypothesis • Alternative hypothesis 1 (a). Null hypothesis: In test of hypothesis We always begin with an assumption. This is called null hypothesis. it is denoted Ho usually. According to R. A. fisher “ the hypothesis which is tested for possible rejection under the assumption that it is true”.

(b). Alternative hypothesis: Any hypothesis different from the Null hypothesis [Ho] is called an alternative hypothesis. It is denoted by H 1. Ho and H 1 both hypothesis are such that if one is accepted, the other is rejected and vice versa. 2 Type 1 Type 2 errors : In process hypothesis we came across same sort of errors , called errors in hypothesis testing which has two types. • Type I errors : Type I errors are made when we reject Ho [Null hypothesis] though it is true. In other words , when Ho is rejected despite its being true , then it is called type I errors.

• Type II errors : Type II errors are made when we accept null when H 0 is accepted despite its being false, then it is called type II errors. 3. Level of Significance : This refers to degree of significance with which we accept or reject a hypothesis. This level is denoted by R. which represent probability of committing type I errors 4. Critical region or rejection region : It is the region of the standard normal curve corresponding to a level of significance. We can say that statistic which leads to rejection of Ho Null hypothesis gives a rejection region. The region under normal curve which is not covered by rejection is Acceptance region.

5. One Tailed test and Two Tailed test : A test of any statistical hypothesis where alternative hypothesis is expressed by [< or >] is called a one tailed test the critical region for symbol [ > ] lies on right tail for symbol [<] on the left tail & the test of hypothesis where alternative is written is called two tailed test. 6. Critical value : The critical value of the standard normal variate [Z] for both two- tailed and one-tailed tests at different level of significance are very often required in hypothesis testing. Procedure of testing a hypothesis • Set up a null hypothesis. • Set up a suitable level of significance. • Set up a suitable test of static. • Doing necessary calculations. • Making decisions.

Applications of test of hypothesis test of significance Applications of test of significance are studied under following headings. • Tests of hypothesis for large samples. • Tests of hypothesis for small samples. • Test of hypothesis for large samples following are application of test. • Test of hypothesis about population. • Test of hypothesis about difference between two population means • Test of hypothesis about difference between two population SD’s • Test of hypothesis about population proportions • Test of hypothesis difference between two population

Hypothesis testing -- small sample test The various tests of hypothesis or test of significance discussed above were related to large samples test of hypothesis relating to large sample are based on two assumptions • sampling distribution approaches a normal distribution • the values are sufficient closed to population values These assumptions are not good for small samples therefore, it becomes necessary to make a separate study of small sample tests various small sampling tests are 1 2 3 1 t-test Fisher z-test F-test t-test is a small sample test. It was developed and. published under the pen name of student. so it is known as students T-test. for this formula is used t= deviation from the population parameter standard error at sample statistic

Fisher z -test. t-test is used to test the significance of the correction coefficient is the value of population correction coefficient is zero if population corr. coeff. = 0 or difference between two simple corr. coeff. are to be used and then fisher z-test is used Application : To test whether an observed value of r differs significantly from some hypothetical value of population correlation coeff. other than zero, the testis used f-test [variance ratio test] f-test is named after the greater statistician an. R. A. fisher f-test is used to test whether the two independent estimates of population variance differ significantly or two sample may be regarded as drawn from normal population have same variance f= larger estimate of population variance

Chi – Square test The Chi -Square is an important test of significance, pronounced as Kisquare. It is used for testing the significance of population variance. As a non – paramedic test it can be used as a test of goodness of fit and as a test of attributes thus chi-square test is applicable for following 1 As a test for population variance 2 As a non – parametric test Property Additive of chi square Chi square possesses additive property if a number of samples of data are collected and a number of chi square values are obtained , then combine them by addition. The table value of chi square 5% level of significance is 3. 841 and 8 d. f is 15. 507 Condition for using Chi Square test is that 1 Sample observation are independent 2 The constraints on cell frequencies are linear 3 No expected frequency should be small i. e. < 5[if e <5. we use pooling technique.

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