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# Hypothesis method

Extracts from this document...

Introduction

## Table of content

TABLE OF CONTENT

INTRODUCTION

Statistical Hypotheses:

Null Hypothesis:

TYPES OF TESTS

ERROR

STEPS IN HYPOTHESIS TESTING

PRACTICAL EXAMPLES

LIMITATIONS FOR ENVIRONMENTAL SAMPLING

SUMMARIZE

FREQUENCIES

HISTOGRAM

DATA VIEW FROM SPSS

VARIABLE VIEW FROM SPSS

## Introduction

There are two types of statistical inferences: estimation of population parameters and hypothesis testing. Hypothesis testing is one of the most important tools of application of statistics to real life problems. Most often, decisions are required to be made concerning populations on the basis of sample information. Statistical tests are used in arriving at these decisions.

## Statistical Hypotheses:

They are defined as assertion or conjecture about the parameter or parameters of a population, for example the mean or the variance of a normal population. They may also concern the type, nature or probability distribution of the population.

Statistical hypotheses are based on the concept of proof by contradiction. For example, say, we test the mean (δ) of a population to see if an experiment has caused an increase or decrease in δ. We do this by proof of contradiction by formulating a null hypothesis.

## Null Hypothesis:

It is a hypothesis which states that there is no difference between the procedures and is denoted by H0. For the above example the corresponding H0 would be that there has been no increase or decrease in the mean. Always the null hypothesis is tested, i.e., we want to either accept or reject the null hypothesis because we have information only for the null hypothesis.

## Types of Tests

Middle

A better method for comparing several population means is an analysis of variance, abbreviated as ANOVA.

ANOVA test is based on the variability between the sample means. This variability is measured in relation to the variability of the data values within the samples. These two variances are compared through means of the F ratio test.

If there is a large variability between the sample means, this suggests that not all the population means are equal. When the variability between the samples means is large compared to the variability within the samples, it can be concluded that not all the population means are equal.

The tests used in the testing of hypothesis, viz., t-tests and ANOVA have some fundamental assumptions that need to be met, for the test to work properly and yield good results. The main assumptions for the t-test and ANOVA are listed below.

The primary assumptions underlying the t-test are:

• The samples are drawn randomly from a population in which the data are distributed normally distributed.
• In the case of a two sample t-test, δ12 = δ22.Therefore it is assumed that s12 and s22 both estimate a common population variance, δ2. This assumption is called the homogeneity of variances
• In the case of a two sample t-test, the measurements in sample 1 are independent of those in sample 2.

Like the t-test, analysis of variance is based on a model that requires certain assumptions.

Three primary assumptions of ANOVA are that:

• Each group is obtained randomly, with each observation independent of all other observations and the groups independent of each other.
• The samples represent populations in which the data are normally distributed.
• δ12 = δ22 = δ32 = ... = δk2. The assumption of homogeneity of variances is similar to the discussion above under the t-test. The group variances are assumed to be an estimate of a common variance, δ2.

Conclusion

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## Frequencies

Figure 7

 Statistics Amount Spent N Valid 30 Missing 2 Mean 320.7333 Std. Error of Mean 41.45531 Median 261.5000a Mode 150.00b Std. Deviation 227.06006 Percentiles 10 77.5000c 20 133.3333 30 204.5000 40 247.5000 50 261.5000 60 346.6667 70 360.0000 80 417.5000 90 687.5000 a. Calculated from grouped data. b. Multiple modes exist. The smallest value is shown c. Percentiles are calculated from grouped data.

Figure 8

 Amount Spent Frequency Percent Valid Percent Cumulative Percent Valid 45.00 1 3.1 3.3 3.3 50.00 1 3.1 3.3 6.7 55.00 1 3.1 3.3 10.0 100.00 1 3.1 3.3 13.3 120.00 1 3.1 3.3 16.7 125.00 1 3.1 3.3 20.0 150.00 2 6.3 6.7 26.7 200.00 1 3.1 3.3 30.0 209.00 1 3.1 3.3 33.3 222.00 1 3.1 3.3 36.7 245.00 1 3.1 3.3 40.0 250.00 1 3.1 3.3 43.3 255.00 1 3.1 3.3 46.7 258.00 1 3.1 3.3 50.0 265.00 1 3.1 3.3 53.3 300.00 1 3.1 3.3 56.7 345.00 1 3.1 3.3 60.0 350.00 2 6.3 6.7 66.7 355.00 1 3.1 3.3 70.0 365.00 1 3.1 3.3 73.3 368.00 1 3.1 3.3 76.7 390.00 1 3.1 3.3 80.0 445.00 1 3.1 3.3 83.3 500.00 1 3.1 3.3 86.7 525.00 1 3.1 3.3 90.0 850.00 1 3.1 3.3 93.3 880.00 1 3.1 3.3 96.7 900.00 1 3.1 3.3 100.0 Total 30 93.8 100.0 Missing System 2 6.3 Total 32 100.0

## Histogram

Figure 9 ## Data View From SPSS ## Variable View From SPSS This student written piece of work is one of many that can be found in our University Degree Statistics section.

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