BB108 Statistical Ways In Assessing Business Issues: Business Statistics Assessment Answer

1. 

a. Most of the time in social related datasets it is very hard to collect the data of a population as population in statistics is termed to infinity. So to determine the relation and parameters for population sample statistics is calculated which gives a close idea of a distribution of population dataset. 

Central Limit Theorem is  been applied in that cases which says that if a population have a mean µ and standard deviation is σ and after taking random samples from the population with replacement , the formed distribution is very approximately close to the sample distribution . This condition holds in either case of normally distributed or skewed with sample size greater than 30. The provided dataset of GmbH have sample size greater than 30 so the mean and standard deviation for these can be very closely related to means and standard deviation of population.

b. There are many ways to create a sample, such as random, systematic or stratified etc. Depending on requirement, situation a hand and characteristics of the data, a sample method can be selected. To create a sample from the data first the sample size is been calculated here the data set of GmbH has a population greater than 30 so after taking random samples with replacement several sample can be created from the determined dataset. Random samples with replacement suggests taking values from the dataset that can be repeated in the main distribution.

c. By considering the Central Limit Theorem, random samples with means µ1, µ2, µ3 ……µn and standard deviations σ1, σ2, σ3 ………σn can be approximately close to the population mean and population standard deviation so the parameter of the ample can be used to evaluate the statistics of the population. By using Central Limit theorem several samples can give a brief about the Population data set.

Major Disadvantages of statistical ways in business issues are

1. Having a small sample size: Most of the businesses are unable to collect the large data which creates problem in decision making and customer segmentation.

2. Low Frequency data: Business should have a large frequency datasets this means they have to collect the data from their clients and customers on the daily basis. This will help in to collect large data and thus increase a good decision making.

Major Advantages of statistical business issues –

1. Performance Management – Performance management is the core of the business. A sufficient data will elaborate the performance of the team of the company thus increasing the decision making capabilities. 

2. Cost Analysis – Statistic can help business to determine the area where they are spending chunks of money. Statistics report also helps business to cut the cost and thus making more profits.

2.

a. The variable salary is quantitative in nature while the variable gender is categorical in nature. Hence, we can compare the means for the two categories to conclude whether salary is gender biased. Hence hypothesis can be created as whether the mean salary for males is different from the mean salary for females.

The null hypothesis and the alternative hypothesis can be formulated as follows:

H0: µ1 = µ2

HA: µ1 ≠ µ2

Where µ1 is mean salary of males and µ2 is mean salary of females.

Two sample T-test was conducted (assuming equal variances):

From above, it can be seen that two tail p-value is 0.5452. If we assume a significance level of 0.05, then p-value is higher than 0.05. This means that the statistical evidence is not significant enough to reject the null hypothesis. Hence, we conclude that the mean salary for males is same as mean salary for females. In other words, we can conclude that salary is not gender-biased.

3.

a. The required output is to test whether training improves job satisfaction. Hence, the variable used will include comparing job satisfaction before training and after training. The hypothesis to be tested is whether mean job satisfaction score before training and mean job satisfaction score after training are different.

b. Hence, mean score will be used to compare. Further, since the variables are dependent and paired, the test to be used is a dependent t-test for paired samples.

The null hypothesis and the alternative hypothesis can be formulated as follows:

H0: µ1 = µ2

HA: µ1 ≠ µ2

Where µ1 is mean job satisfaction score before training and µ2 is mean job satisfaction score after training

c. A significance level of α = 0.05 has been assumed.

d. Using MS-Excel, paired t-test for means (assuming equal variances) has been conducted as follows: 

In both manual and excel calculations, it can be seen that t-stat is 17.31278

e. The above conducted test reveals a p-value of 0.0000 which is lower than the assumed significance level of 0.05. Hence, there is sufficient evidence to reject the null hypothesis. It can be concluded that there is significant difference in job satisfaction score before and after the training. Hence, training impacts job satisfaction score. In this case, two-tailed test was used.

Alternatively, a one-tailed test can be used where the hypothesis can be formulated as follows:

H0: µ1 > µ2

HA: µ1 < µ2

Where µ1 is mean job satisfaction score before training and µ2 is mean job satisfaction score after training

In this case, one tailed p-value must be considered, which is again 0.00000, that leads to rejection of null hypothesis.

4. 

a. 

The above graph indicates a linear positive relationship between the two variables as indicated by the trend line and concentration of data points also. As salary increases, life happiness score also increases and vice versa.

b. 

The above graph indicates no relationship between the two variables as it seems that life happiness score varies irrespective of the job satisfaction score after training which seems irrelevant.

d. The value of correlation coefficient R is 0.95 while R square is 0.91. This indicates that there is a strong positive relationship between the dependent and independent variables. Also R square indicates that as much as 91% of variation in dependent variable can be explained though selected independent variables. 

• The regression equation is y = -7.8865 + 0.1884 x1 + 1.1478 x2 

Where: Y is life happiness score, x1 is salary and x2 is job satisfaction score after training.

• The significance F is 0.0000 which is lower than assumed significance level of 0.05. This indicates that the created regression model is a good fit.
• Each of the independent variables also have low p-values (lower than 0.05). This indicates that variables are relevant to the predicted variable.

5.  Based on the above analysis, it was seen that there is no difference in mean salaries of males and females. Hence, the salary is not gender biased. 

It was seen that job satisfaction score is impacted by training and the score improves tremendously as seen through statistical testing and is also evident in mean score before training which was 2.10 and mean score after training which was 3.54. Hence, job satisfaction improves tremendously after training.

It was also found that there is a strong positive relationship between life happiness score and salary. As salary increases, life happiness score also increases. Similarly, as salary decreases, life happiness score also decreases. However, the scatterplot for job satisfaction score after training and life happiness score does not indicate linear relationship. The scatterplot indicates a pattern of horizontal data clusters that seems to indicate that job satisfaction score after training is irrelevant to the level of life happiness score. Alternatively, the relationship might be non-linear in nature.

A regression analysis was performed for predicting life happiness core (predicted variable or dependent variable) based on salary and job satisfaction score after training (predictor variables or independent variables) and it was found that there is a strong relationship between the said variables as indicated by high positive value of R 0.95. The regression model created was also seen to be a good fit as indicated by high R-square value of 0.91 and also by p-value of 0.0000 which is lower than significance level of 0.05. Further the independent variables were also found to be significant as indicated by the low p-values.

Hence, it can be said that job satisfaction is an important variable that can be meaningfully accentuated through training. Additionally, job satisfaction impacts variables such as life happiness score. Another important variable is salary that impacts life happiness score also