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Unit 9

Unit 9

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

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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.

The smaller the difference, the greater the likelihood that our hypothesised value for the parameter is correct. The larger the difference, the smaller the likelihood that our hypothesised value for the parameter is correct. Unfortunately, the difference between the hypothesised population parameter and the actual statistic is more often; neither so large that we automatically reject our hypothesis, nor so small that we just as quickly accept it. So in hypothesis testing, as in most significant real-life decisions, clear-cut solutions are the exception, not the rule.

Objectives:

After studying this unit, you should be able to:

describe the basic concepts of testing hypothesis

describe the different test statistics available

identify the test for a given problem

identify the type of errors

9.1.1 Relevance

Caselet

You need to be objective

The government in a certain country says that radiation levels in the area surrounding a nuclear power plant are well below levels considered harmful. Three people in the area died of leukemia. The local people immediately put the blame on the radioactive fallout. Does the death of three people make us assume that the government is wrong with its information and that we make assumption or hypothesis, that radiation levels in the area are Sikkim Manipal University

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abnormally high? Alternatively, do we accept that the deaths from leukemia are random and not related to the nuclear power facility? You should not accept or reject a hypothesis about a population parameter- in this case the radiation levels in the surrounding area of the nuclear power plant, simply by institution. You need to be objective in decision making. For this situation an appropriate action would be to take samples of the incidence of leukaemia cases over a reasonable period of time and use these to test the hypothesis. The purpose of this unit is to find out how to use hypothesis...