# IP3

Introduction

In order to determine whether the sample and its statistics may be treated as representing the whole population, it is necessary to define whether the sample of the mean does not significantly differ from the sample of the population. Generally, for testing one sample means null hypothesis is stated as “means are equal”, and alternative hypothesis is “means are not equal” (two-tailed hypothesis).

The aim of this research is to analyze whether the values of intrinsic and extrinsic job satisfaction listed in AIU demographic survey can be used to represent the whole population of AIU employees, i.e. whether the mean of intrinsic and extrinsic job satisfaction samples do not differ significantly from appropriate means of the whole population.

Description of methods

There are two types of test for hypothesis test for a single population mean of a quantitative variable equal to a given number: t-test and z-test. T-test is applied best when the sample size is limited and is less or equal to 30; z-test is more appropriate for larger samples with N>30 and fro samples where the standard deviation of the population is known (Dalgaard, 2008). In general, t-tests have fewer limitations compared to z-tests, and are more adaptable, but they have more fluctuations. However, t-tests are more commonly used than z-tests (Dalgaard, 2008). For testing null and alternative hypotheses for a single sample two-tailed t-test will be applied.

Results

The t-statistic will be calculated using the following formula (Salkind, 2010): where is the sample mean, is the suggested population mean, s – standard deviation of the sample, and n – sample size. Table 1 shows auxiliary values used for calculating t-statistics and final t values for intrinsic and extrinsic job satisfaction.

In order to determine whether null hypothesis is true, it is necessary to find out critical t-values for 24 degrees of freedom (N-1 = 24), and find out p-value, i.e. the value that null hypothesis should be accepted. Table 2 contains the necessary data and the decisions.

Interpretation of results

Since both of t-values appeared to exceed the critical value (and p-values were below the chosen significance level of 0.05), it is possible to state that both null hypotheses have to be rejected. Thus, for the whole population mean of intrinsic job satisfaction is not equal to 5; also, the mean of extrinsic job satisfaction is not equal to 5. However, it is possible to determine that extrinsic job satisfaction is more close to 5 than intrinsic job satisfaction.

Conclusion

Statistical analysis in the form of two-tailed single sample test has shown that neither extrinsic nor intrinsic employees’ job satisfaction means is equal to 5. However, since two-tailed t-test was used, no more conclusions about the values of means can be done. In general, t-test is a powerful and flexible instrument of studying the samples and making decisions concerning the chosen population.

References

Dalgaard, Peter. (2008). Introductory statistics with R. Statistics and computing.
Salkind, Neil J. (2010). Encyclopedia of Research Design. SAGE.

IP3 9.2 of 10 on the basis of 2020 Review.