Abstract
The paper performs t test analysis to test the hypothesis for the dataset used for the statistical purpose. Inferences have been derived regarding the intrinsic and extrinsic satisfaction by gender and position respectively to accept or reject the null hypothesis. Tabulated representation of the analysis data is displayed for the interpretation of the results in the paper.
Introduction
T test is performed to accept or reject the null hypothesis in the paper. The intrinsic and extrinsic satisfaction of the employees is tested through the two sample t-test. The data is hypothesized to test that the intrinsic job satisfaction of the male employees is similar to female employees and the extrinsic satisfaction of hourly employees is similar to that of salaried employees. Along with performing the test for acceptance or rejection of null hypothesis, the managerial application of the result is also explained in the paper.
Hypothesis Test-1: Looking at Intrinsic Satisfaction by Gender
Null and Alternate Hypothesis
Null Hypothesis: The mean level of intrinsic job satisfaction for the male employees is equal to that of the female employees.
Alternate Hypothesis: The mean level of intrinsic job satisfaction for the male employees is not equal to that of the female employees.
The Test:
We shall use t-test for two samples to test the given hypothesis.
We shall use significance level, α = 0.05.
Since the alternative hypothesis is, the given test is a two-tailed t-test.
For from Student’s t-distribution the critical values of the two-tailed t-test are.
Decision Rule:
t-Test: Two-Sample Assuming Unequal Variances
Male
Female
Mean
5.136363636
5.314285714
Variance
0.612900433
0.213626374
Observations
22
14
Hypothesized Mean Difference
0
df
34
t Stat
-0.856840225
P(T<=t) one-tail
0.1987662
t Critical one-tail
1.690924198
P(T<=t) two-tail
0.3975324
t Critical two-tail
2.032244498
State the Decision:
Since, < t-critical, we fail to reject the null hypothesis. Applications for Managers: The managers can conclude that the intrinsic job satisfaction levels do not significantly vary with the gender of employees. Hypothesis Test-2: Looking at Extrinsic Satisfaction by Position Null and Alternate Hypothesis Null Hypothesis: The mean level of extrinsic job satisfaction for the hourly employees is equal to that of the salaried employees. Alternate Hypothesis: The mean level of extrinsic job satisfaction for the hourly employees is not equal to that of the salaried employees.
The Test:
We shall use t-test for two samples to test the given hypothesis.
We shall use significance level, α = 0.05.
Since the alternative hypothesis is, the given test is a two-tailed t-test.
For from Student’s t-distribution the critical values of the two-tailed t-test are.
Decision Rule:
t-Test: Two-Sample Assuming Unequal Variances
Hourly Employee
Salaried Employee
Mean
5.37826087
5.476923077
Variance
0.179960474
0.358589744
Observations
23
13
Hypothesized Mean Difference
0
df
19
t Stat
-0.524323031
P(T<=t) one-tail
0.303058742
t Critical one-tail
1.729132792
P(T<=t) two-tail
0.606117484
t Critical two-tail
2.09302405
State the Decision:
Since, < t-critical, we fail to reject the null hypothesis. Applications for Managers: The managers can conclude that the extrinsic job satisfaction levels do not significantly vary with the position of employees. Z-test and T-test are both parametric hypothesis tests. A z-test is preferable when the sample size, n > 30. If the sample size, n < 30, a t-test is preferable. According to the Central Limit Theorem, for small sample sizes, the t-distributions and z-distributions are different. As sample sizes gets above 30, the t- distributions and z-distributions become similar.
t Stat
+++++++++
t Stat
+++++++++*
A population refers to the whole group or complete set of individuals about which inferences are to be made and are typically very large (Johnson and Bhattacharyya, 2009). Therefore considering all the individuals in the population for a survey is impractical or impossible and can be very expensive. Therefore, samples or sub-sets are taken from the population, representing a manageable size of the population, and the statistical observations are made on these samples (Brase and Brase, 2011).
t Stat
++++
The t-test conducted in the paper concludes that intrinsic job satisfaction does not vary with gender of the employees and the extrinsic job satisfaction does not vary with the position of the employee. The paper also describes between the z test and t test and provides the reasoning for using samples instead of populations.
t Stat
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Charles Henry Brase and Corrinne Pellillo Brase. (2011). Understandable Statistics: Concepts and Methods. Boston, MA: Cengage Learning.
Glenberg, A. M. (1996). Learning from data: an introduction to statistical reasoning. Mahwah, New Jersey: Routledge.
Mittelhammer, R. (1996). Mathematical statistics for economics and business. Pullman, WA: Springer.
Richard A. Johnson and Gouri K. Bhattacharyya. (2009). Statistics: Principles and Methods. John Wiley and Sons.
Sá, J. P. (2003). Applied statistics: using SPSS, STATISTICA, and MATLAB. New York: Springer.
