In the last year, an organization made an annual profit of £1203 per employee while the average for organizations within the sector is £1228 per employee. The sector had a standard deviation of £104 per employee. We are required to use the data to carry out hypothesis and determine whether there is an evidence that the organization is on average not as profitable as the competitors.
Answers to Questions
- State the null and the alternative hypothesis to prove the claim.
The null hypothesis is the expression of equality that will indicate that there is no difference from the given specification (Bruce, 2015). In this case it will indicate that there is no difference between the organization’s profit and that of the sector. The alternative hypothesis is the compliment of the null hypothesis indicating non-equality or difference from a given specification (Bruce, 2015). In this case, since we want to know whether the profit is less than that of other sector, it will have a greater than or equal to sign indicating that if the null hypothesis is not true, then the profit of the organization is greater than that of competitors. The expression can be summarized as:
- With the assumption that the profit per annum per employee follows a normal distribution and the resulting P-value from the hypothesis test is, P=0.405 (3 d.p). What can we conclude from the test?
The p-value indicates the probability of the null hypothesis being true or otherwise being false (Croucher, 2016). In this a P-value of 0.405 is quite high and therefore we cannot reject the null hypothesis. Therefore, we conclude that there is no sufficient evidence that our organization is less profitable compared to the other organizations within the sector.
- The probability of obtaining a profit of or less than £1203 per employee where there exists no statistically significant difference between the organization and the sector average.
We first determine the z-score using the formula:
Where z is the z-score, x is the value of profit in our organization, µ is the mean profit of the sector and is the standard deviation of the sector.
The probability required can be expressed as:
To find the value of the probability we check from the standard normal table for the value of Z-score is equal to -0.24. We get:
Therefore, the probability of getting a profit equal or less than £1203 is 0.4052.
- If the profit of each employee per year gave a P-value of 0.032 and the significance level was 0.01 what can we conclude and why?
Significance level is the value of the boundary of the area below which a given P-value indicates significant evidence in favor of the alternate hypothesis and against the null hypothesis (Selvanathan and Keller, 2017). In this the significance level of 0.01 is much less compared to the p-value of 0.032 therefore, we cannot reject the null hypothesis and we can conclude that there is no sufficient evidence that our organization makes less profit compared to the competitors within the sector.
- If the null hypothesis was rejected when it was actually true what type of error would be committed?
Type I error is the error that is committed when a true null hypothesis is rejected. On the other hand, a type II is error committed when we fail to reject a false null hypothesis (Hinton, 2014). In this we the null hypothesis was true and it was rejected a Type I error would have been committed.
- Assumptions made about the annual profit per employee in the hypothesis test.
Since the hypothesis test in statistics is parametric, it will assume that the population from which the data is collected has certain specific characteristics and that that the sample is drawn under certain specified conditions (Hinton, 2014). In this case, since we are using Z-statistical test, the assumptions made are that the distribution of the annual profit per employee is normally distributed and was obtained from random sampling of a defined population.
Bruce, P. (2015). Introductory statistics and analytics. New Jersey: Wiley.
Croucher, J. S. (2016). Introductory mathematics & statistics. 6th ed. Australia: North Ryde, N.S.W. McGraw-Hill Education.
Hinton, P. R. (2014). Statistics explained. 3rd ed. London: Routledge, Taylor & Francis Group.
Selvanathan, E. A., and Keller, G. (2017). Business statistics abridged. 7th ed. South Melbourne, Victoria: Cengage Learning.