Course Outline

·        Basic concepts: Null hypothesis, Alternative hypothesis, One-tailed and two-tailed tests, Type I and Type II errors, Level of significance, Critical region, Value, Test statistics, Steps in hypothesis testing.

·        Z-test: Difference between two means of large samples with unknown population variance.

·        T-test: Difference between two means of small samples with unknown common variance.

·        Chi-square test: Significance test of independence.

·        Significance test for correlation coefficient.

Introduction

·     Hypothesis: On the basis of sample information, we make certain decisions about the population. In making such decision, we make certain assumptions. These assumptions are known as statistical hypothesis. These hypothesis are tested. Assuming the hypothesis correct we calculate the probability of getting the observed sample. If this probability is less than a certain assigned value, the hypothesis is to be rejected.

·     Null hypothesis: Null hypothesis is the hypothesis of no difference. The null hypothesis asserts that there is no difference between the statistic and the population parameter and whatever observed difference is there is merely due to fluctuations in sampling from the same population. Null hypothesis is usually denoted by the symbol H0.

·     Alternative hypothesis: Rejecting null hypothesis implies that it is rejected in favour of some other hypothesis which is accepted when H0 is rejected is called alternative hypothesis and is represented by H1. Alternative hypothesis can be two sided or one sided. The alternative hypothesis represents the conclusion that would be reached if there were sufficient evidence from sample information to decide that the null hypothesis is unlikely to be true and we can therefore reject it.

Example: The null hypothesis is H0: m = m0 and

          Alternative hypothesis may be

i)       H1 : m ¹ m0 (i.e. m > m0 or m < m0) (Two tailed)

ii)     H1 : m > m0 (right tailed)

iii)    H1 : m < m0 (left tailed)
























21.   In a random sample, 74 of 250 persons who watched a certain television program in black and white and 92 of 250 person who watch the same program in coloured remembered 2 hours letter what product were advertised. Use chi-square statistics to test the null hypothesis q1 = q2 against the alternative hypothesis q1 ¹ q2 at the 0.01 level of significance.

Soln:   As in Q. No. 10