HYPOTHESIS TESTING

Table of Contents

Introduction…………………………………………………………………………………….3

Data Fields………………………………………………………………………………………3

Preliminary Data Analysis………………………………………………………………………3

Data Analysis……………………………………………………………………………………7

Independent T-Test Results……………………………………………………………………..7

Hypothesis Testing………………………………………………………………………………9

References……………………………………………………………………………………….9

Introduction

In this report we analyze the wellbeing and certain other indexes of the life style, from a sample of 200 data points of a population of over 950 State School Teachers in late 1980s, which may be either the primary or secondary school teachers in Victoria. The report has used the independent T-tests, Regression Analysis and Annova techniques to reach the results for the sample.

The Data fields

The following is brief overview of the data fields or variable for the sample.

This was a brief description of the variable being used to describe the samples in the report.(Dean 2010)

Preliminary Analysis of Data

We did a few initial analysis of the data presented with the help of graphs. At first we plotted a linear regression graph of well being of the teachers with the lifestress variable. As it is known that there should be a negative relationship between the two data. Thus, graph comes out to be:

This shows a linear but downward slopping relation-ship between the variables, which matches our expectations. Now, Let us try the relationship of misbehavior of the students and the wellbeing and negative life event stressors. From the following two graphs in the next page it is clear that the student’s misbehavior is one of the negative factors in the life of the teachers. The relationship between the General well being of the teachers with the level of misbehavior shows a downward trend in the graph, that is the graph has negative slope similar to what we had in the previous one. This is again manifested by the next graph between the negative life stressors and the misbehavior of students. The two variables have a strong relation-ship, shown by the linear curve with a positive slope. (Buglear 2010)

There is another negative factor in the life of the teachers which is the job ambiguity, representing the uncertainty about the future. This has been plotted in the graph 4.

Thus, as shown in the above graph the stress increases with the future uncertainty. This is a causative result from the linear graph. But, let us have a look at the coefficient of determination; weather the curve has statistic support. (Boslaugh, 2011)

In all the above three summary tables about the relation ship curves, we discussed the value of R square is very low. Since the coefficient of determination has a very small value in all the above cases, it can be said the statistic evidence fort the curves to be true is very low.

Now, let us do some hypothesis testing and t-tests and the other tests (Annova) to have an analysis of the whole data taken together.

Data Analysis

• The Regression analysis: The regression analysis give the best curve fitting of  the given samples of data. The regression analysis table is given as below:

Thus, if we assume that the curve of relationship between the state of a teacher and the other variables can be represented by a linear curve, we can represent it with the help of a linear equation.

The values of the coefficients () and the intercept ant the error can be taken from the table and the relationship can be framed as:

Thus is the relationship curve of the state of the teacher in terms of the variables. This is to be noted that the coefficient of higher values have greater influence over the curve.

Independent T-test Results

The t-test with independent samples gives the difference between the parameters of the sample and the population with the assumption that the two samples have the same or approximately same values of variance. However, t-test with unequal variances can be also calculated. The T-test results table is shown below:

The t-values have been calculated with significance level  for the right tailed distribution. The t-values can be used to do hypothesis testing of the variables. Suppose the null hypothesis stands as well being of the teachers with age group less than 40 is better than teachers with age group above 40.

Hypothesis Testing

Thus, , where is the mean well being of the teachers below 40 years and  is the age of teachers above age of 40. Since the value of the t-test is very low in the significant region so, we do not have enough reasons to fail the null hypothesis.

The values of t-test which are less than zero signify the parameters of the sample are less in compared to the values of the population.

References

1. Advanced Statistics, viewed on 11^th may 2012, www.statmethods.net/advstats/index.html

2. IBM SPSS User Guide 17

3.Advanced Statistics for dummies, viewed on 11^th may  www.dummies.com/…/Statistics-II-for-Dummies.productCd-0470466

4.Statistics, Probability and Survey Sampling: http://stattrek.com/

5. Buglear Jon 2010,Statistics Means Business-A guide to business statistics

6. Sarab Boslaugh & Paul Andrew waters 2011,

Statistics in Nutshell:  Orielly Publication

7 Robert A.Stine and Dean FosterStatistics for Business: Decision making and Analysis Pearson Publication

8. Advanced Statistics Demystified. by Larry J Stephens (TMH)

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