Comprehensive Business Statistics Analysis Report - MA108

This report presents a comprehensive business statistics analysis, examining various factors related to employee job satisfaction and other business variables. The analysis includes the comparison of variance and standard deviation of job satisfaction before and after training, covariance between job satisfaction and life happiness, and independent sample t-tests to determine differences in life happiness scores between male and female staff. Z-score analysis is used to identify outliers in salary and age data. Furthermore, the report employs chi-square tests to assess the relationship between marital status and promotion, correlation analysis to examine the relationship between years of experience and salary, and regression analysis to determine the impact of salary on life happiness. The results indicate that while training and other variables did not significantly affect life satisfaction, promotion showed a significant difference based on gender. The report concludes with recommendations for the company to focus on promotion practices, ensuring equal opportunities for all employees, regardless of their gender, to improve overall job satisfaction.

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Name
Institution
Course

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Introduction
The analyses to be conducted are to compare the standard and variance between job satisfaction before
training and after training. To determine covariance between the job satisfaction score before training’
and life happiness score and to show whether they change in the same direction. To conduct an
independent sample T-test by determining whether there is a statistically significant difference in ‘life
happiness score' between two groups of male and female staff. To conduct a Z-score analysis to
determine how many standard deviations are above or under average ‘Salary’ and ‘Age’ area and
whether there are any outliers. To carry out a chi-square to test whether there is a difference between
marital status and promotion. To determine the correlation between the years of experience and the
salary. Finally, to conduct a regression analysis to determine whether salary determined life's
happiness.
Problem definition and business intelligence
The real problem is focused on is the employees' job satisfaction. It was found that employees' job
satisfaction had been deteriorating. A research was conducted to determine the job satisfaction of the
employees. This aimed to improve employees’ satisfaction from the results of the analysis. The analysis
techniques to be used to study the data are correlation, regression, chi-square test and Independent
sample T-test.
Variance/ Standard deviation
The objective of this section is to compare the standard deviation and variance difference between job
satisfaction before and after training.
Table 1: Standard deviation and variance of job satisfaction before and after training

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Table 1 shows the variance and the standard deviation of the job satisfaction before and after training.
The difference of standard deviation between job satisfaction before and after training is 0.127. The
difference between the variance of the job satisfaction before and after training is 0.259. These results
show that there is no meaningful difference between them.
Covariance
Table 2: Covariance between job satisfaction before the training and the life happiness
From Table 2, the covariance between Job satisfaction before training and Life happiness obtained is
0.230. The two variables vary in the same direction because the value of the covariance is positive.
Independent sample T-test
The aim of this part is to determine the statistically significant difference in ‘life happiness score'
between two groups of male and female staff.
Table 3: Independent sample T-test of life happiness score and the gender of the staffs

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Table 3 shows the Independent sample T-test of the life happiness score and the gender. To give a
deduction of the test, the hypothesis should be formulated under which the test will be used to validate
the hypothesis.
Formulation of hypothesis
There is no significant difference in life happiness between genders – the null hypothesis
Testing the hypothesis
To test the hypothesis, the significant value is compared to the p-value (0.05). The significant value from
Table 3 is used to conduct the test. If the significant value is greater than the p-value, then the null
hypothesis is accepted. Otherwise, we reject it. In this case, the significance value is 0.997. Since it is
greater than 0.05, we accept the null hypothesis and conclude that there no significant difference in life
happiness between genders.
Z-score test
The aim of this part is to determine how many standard deviations are above or under average ‘Salary’
and ‘Age’ and whether there are any outliers.
Table 4: Z score of Age and Salary
The results from table 4 show that there was no standard deviation and age that were above or below
the average salary and the age. The mean and standard deviation obtained (M =0, SD = 1) shows that
the shape of the two variables was normal and therefore, there was no outlier in the data.
Chi-square test
The aim of this part is to determine whether there is any relationship between ‘marital status’ and
‘promotion. To test this question, the chi-square test is to be conducted on marital status and
promotion. The hypothesis will be formulated, and the result obtained from the test is used to validate
the results. Below is the result from the test.

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Formulation of hypothesis
There is no significant relationship difference between promotion and marital status – the null
hypothesis
Testing the hypothesis
To test the hypothesis, the focus will be on the significance value. If the significance value is below 0.05,
then we reject the null hypothesis. Otherwise, it is accepted. In this scenario, it is below 0.05, and
therefore, the null hypothesis is rejected. Thus, one can deduce that there is a significance difference in
promotion and marital status (Test, 2015).
Correlation analysis
The aim of this part is to determine whether there exists a statistically significant relationship between
‘years of experience’ and ‘salary’. Correlation analysis determines the association of two variables.
Below is the output of the correlation analysis.
Table 5: Correlation between the years of experience and salary

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Formulation of hypothesis
There is no significant relationship between the years of experience and the salary – null hypothesis
Testing of the hypothesis
To test the hypothesis, the significant value will be used. From Table 5, the significant value is 0.961
which is above the p-value and therefore, the null hypothesis is accepted. Hence, it is deduced that
there is no significant relationship between the years of experience and the salary.
The correlation value obtained (.003) means that the relationship between the two variables is 3 %
which is very low.
Regression Analysis
The aim of this part is to determine whether salary determined life happiness. In this case, life
happiness is taken as dependent variable and salary to be an independent variable. The general
equation of regression is given by:
y = mx + c, Where y is the dependent variable, x is the dependent variable, m is the gradient and
c is the y-intercept.
Below is the result of the regression analysis.
Table 6: Regression Analysis to show the effect of salary to life happiness
Results from table 6 give the coefficient of regression output. The equation can be summarized as:
Life happiness = 5.598 – 0.02* (Salary)
This means that a score of 5.598 is not affected by salary; it also shows that an increase in a unit of
salary reduces the life happiness by 0.02.
Formulation of hypothesis
Salary has no significant influence on one's life happiness
Testing of the hypothesis

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The significant value obtained from the regression analysis (.424) shows that there was no significant
influence of salary increase in life’s happiness. Therefore, the null hypothesis is accepted (DeFusco et al.
2015).
Results and Recommendations
From all the analysis conducted, all the factors didn't affect life's satisfaction. This included the training
and other variables. Only one test showed a positive result, and that was the promotion. It was
determined that there was a significant difference in promotion within the gender. A company should
focus on promotion to increase job satisfactorily. A company should not discriminate their staffs
according to their sex when it comes to giving promotion.

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References
DeFusco, R. A., McLeavey, D. W., Pinto, J. E., Anson, M. J., & Runkle, D. E. (2015). Quantitative
investment analysis. John Wiley & Sons.
Test, O. (2015). Your chi-square test is statistically significant±now what. Pract Assess Res Eval, 20(8), -
10.