## Question:

## Answer:

### Framing H_{1 }and H_{0} for Hypothesis Testing

_{0 }(Null Hypothesis) - The organisation is not profitable on average as the competitors.

_{1 }(Alternative Hypothesis) - The organisation is profitable on average as the competitors.

Year | Per-Employee Profit (in Pounds) | Industry Profit (in Pounds) | |||||

1 | 970 | 1030 | |||||

2 | 1090 | 1000 | |||||

3 | 1203 | 1228 | |||||

4 | 900 | 916 | |||||

5 | 1050 | 1310 | |||||

6 | 1170 | 1350 | |||||

Anova: Single Factor | |||||||

SUMMARY | |||||||

Groups | Count | Sum | Average | Variance | |||

Per-Employee Profit (in Pounds) | 6 | 6383 | 1063.833333 | 13432.16667 | |||

Industry Profit (in Pounds) | 6 | 6834 | 1139 | 32522.8 | |||

ANOVA | |||||||

Source of Variation | SS | df | MS | F | P-value | F crit | |

Between Groups | 16950.08333 | 1 | 16950.08333 | 0.7376823252 | 0.4105195911 | 6.388176471 | |

Within Groups | 229774.8333 | 10 | 22977.48333 | ||||

Total | 246724.9167 | 11 |

Table 1: Anova testing

(Source: as done by the researcher)

Note: This is a table created by the researcher in order to easy the problem of lack of data in the case study. Here the two variables that is Pre-Employee profit of 1,203 pounds and Industry Profit of 1,228 pounds are being taken from the case itself and the rest of the values are fictitious. Based on the values the P-Value is calculated through Anova analysis and the level of the same is kept as close as possible to the case.

### Conclusion base on P-Value for the test

In the given case it is mentioned that the P-value to be equal to 0.405 or 0.41 if rounded off as given in the table. However, it is to be mentioned by Seber (2015, p.122) that the P-value of 0.0499 is enough to reject the null hypothesis. Therefore if the given P-Value is taken into consideration in order to perform the test then it can be seen that the P-value is quite higher than the level of rejection. Therefore, the null hypothesis (H_{0}) mentioning that the organisation is not profitable on average as competitors should be rejected. On the other hand, it is to be assumed that the alternative hypothesis (H_{1}) stating that the organisation is profitable on average as the competitors is to be accepted.

Therefore, it may be inferred that the organisation is profitable compared to the investors.

### Probability of profit making when the company and the industry per-employee payment can not statistically differentiated

If the pre-employee payment for the company cannot be differed for the company and the industry then the P-value in that case would be equal to 1 which is higher than the minimum range of 0.0499. So, Null Hypothesis (H_{0}) will be rejected and it should be inferred that the organisation can earn the desired level of profit per employee of 1,203 pounds if not more than that. But the desired profit per employee will not go below that level.

### Conclusions based on changed P-value and significance level

In the given case study the significant level is 0.01 and the P-Value given is 0.032, if we take the normal 0.05 level of significance then the minimum level of 0.04993 is needed to reject the null hypothesis (H_{0}). However, this minimum level will be much lower in case of 0.01 level of significance (Murphy et al. 2014, p.125). Hence, the H_{0} can be accepted and it can be concluded that the organisation is not profitable as compared to its competitors, if the P-Value does not exceed the minimum level. However if the P-value is more than the minimum level then the alternative hypothesis (H_{1}) will be accepted and the inference of the organisation being profitable than its competitors will be drawn.

### Type I and Type II error determination based on the rejection of H_{0} scenario

According to Wilcox (2012, p.35) Type I error occurs when the Null Hypothesis is rejected although it is true, and Type II error occurs when the Null Hypothesis is accepted even though it is not true.

In the given scenario if Null Hypothesis (H_{0}) is rejected even being true then the Type I error will occur.

### Assumptions made about the annual per employee profit in this test

In order to answer the questions a table is being prepared by the researcher based on various assumptions on the annual per-employee profit level. The per-employee profit level affects the P-Value (Lukic, 2015, p.10). With the increase in the per employee profit for the organisation the P-Value also increases and vice versa. A reverse effect falls on the P-Value by the increase or decrease in the industrial profit level. So in order to reach the level of 0.405 or 0.41 (rounded off) various adjustments needed to be made. The employee profit level is always less as compared to the industrial profit level as given in Table 1 except for year 2. It is assumed that always the firm is running at a lower level of profit than the industry profit margins.

## Reference List

Seber, G., (2015). The Linear Model and Hypothesis. New York City: Springer.

Murphy, K.R., Myors, B. and Wolach, A., (2014). Statistical power analysis: A simple and general model for traditional and modern hypothesis tests. Abingdon: Routledge.

Wilcox, R.R., (2012). Introduction to robust estimation and hypothesis testing. Cambridge: Academic Press.

Lukic, R., (2015). “The Analysis of Profit per Employee in the Trade of Serbia”.Economia. Seria Management, 18(1), pp.5-16.