Presented by-Tanu Priya

MEANINGHypothesis means a mere assumption or some supposition to

be proved or disproved.Research hypothesis is a predictive statement, capable of being

tested by scientific methods, that relates an independent variable to some dependent variable. Eg. “Students who receive counseling will show a greater increase in creativity than students not receive counseling”.

OR “The automobile A is performing as well as automobile B”.

BASIC CONCEPTS CONCERNING TESTING OF HYPOTHESIS

NULL HYPOTHESIS AND ALTERNATIVE HYPOTHESIS-

If we are to compare A with method B about its superiority and if we proceed on the assumption that both methods are equally good, then this assumption is termed as the null hypothesis and if we assume that method A is superior or method B is inferior, than this assumption is termed as alternative hypothesis.Null hypothesis is symbolized as H₀ and the alternative hypothesis as Hₐ.

THE LEVEL OF SIGNIFICANCE-

The probability of a false rejection of the null hypothesis in a statistical test. Also called significance level.

Eg. In case if we take the significance level at 5 per cent, this implies that H₀ will be rejected when the sampling result has a less than 0.05 probability of occurring if H₀ is true.

TYPE 1 AND TYPE 2 ERROR

ACCEPT H₀ REJECT H₀

H₀(TRUE) Correct decision

Type I error(α error)

H₀(FALSE) Type II error(β error)

Correct decision

DECISION

When we reject H₀ when H₀ is true it is called type I error.When we accept H₀ when it is false it is called type II error.

TWO TAILED AND ONE TAILED TEST

A two tailed test reject the null hypothesis if, say the sample mean is significantly higher or lower than the hypothesised value of mean popullation.

Symbolically, the two tailed test is appropriate when we have H₀:μ=μH₀ and Hₐ: μ≠ μH₀ which may mean μ> μH₀ or μ< μH₀.Thus, in a two tailed test, there are two rejection regions.

A one tailed test is used when we have to test whether population mean is either lower than or higher than some hypothesised value. In this if the rejection region on the left it is called left tailed test .It is represented as- H₀: μ= μH₀ and Hₐ: μ< μH₀

If the rejection is on the right side it is called right tailed test.It is denoted by H₀: μ= μH₀ and Hₐ: μ> μH₀

Some of the important tests are

1. z test 2. t test3.χ2 4. F testz -test- it is based on normal distribution and is used for judging the significance of several statistical measures, particularly the means.t –test- it is based on t- distribution and is considered an appropriate test for judging the significance of difference between the mean of two samples in case of small samples when population variation is not known. χ2- it is used as a parametric test is used for comparing a sample variance to a theoretical population varince.F-test- it is used to compare the variance of the two independent samples.