Testing of Hypothesis in Case of Large
and Small Samples

Structure:
9.1 Introduction
Objectives
Relevance
Assumptions
9.2 Testing Hypothesis
Null and Alternate hypothesis
Interpreting the level of significance
Hypothesis are accepted and not proved
9.3 Selecting a Significance Level
Preference of type I error
Preference of type II error
Determine appropriate distribution for the test of Mean
9.4 Two–tailed Tests and One–tailed Tests for Mean
Case study on Two–tailed and One-tailed tests
9.5 Classification of Test Statistics
Statistics used for testing of hypothesis
Test procedure
How to identify the right statistics for the test
9.6 Testing of Hypothesis in the Case of Small Samples
9.7 ‘t’ Distribution
Uses of ‘t’ test
9.8 Summary
9.9 Glossary
9.10 Terminal Questions
9.11 Answers
9.12 Case Study

9.1 Introduction
In the previous unit, estimation, we have studied about the estimation of the parameter from the samples and the methods of estimation. In this unit, Testing of hypothesis, we will study about hypothesis and the testing of hypothesis. Estimation is about estimating the parameters and finding out Sikkim Manipal University

Page No. 359

Statistics for Management

Unit 9

the confidence intervals. Hypothesis testing is the opinion about the population parameter that may or may not be in the confidence interval derived from the sample. Hypothesis testing is helpful in decision making. Before starting this unit, let’s refresh the concepts we have studied on estimation.

Hypothesis testing begins with an assumption, called hypothesis that we make about a population parameter wherein we assume a certain value for the population parameter. To test the validity of our assumption, we gather sample data and determine the difference between the hypothesised value and the actual value of the sample statistic. Then we judge whether the difference is significant.

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