It is evident from the SPSS data, that the number of observations that are being used in this paper is 51. The descriptive statistics of the various factors that are being considered tell us a lot about the situation of the company. However, without the inferential statistic testing, it will be very difficult for the observers to make claims about any issues that can be seen by looking at the descriptive or raw data.
The summary of the descriptive statistics tell us that over the 12 months period, there has been a great variation in the number of the employees in the company. The number of employee ranged from 5-46 with a standard deviation of 7.49 employees. Another important statistic is the injury rate in the company. Again there has been great variation in the injury rate. It has ranged from 0 to 76 injuries per 100 workers with mean of 15 injuries per 100 workers. Another important factor is the risk of the operational activities. 1 being the lowest risk, and 7 being the highest risk, the mean risk of company’s task is 4 which signifies that the most of the jobs in the company are medium risk.
There can be two hypotheses that can be determined from the descriptive statistics of the data. These can then be checked using the t-test in order to make the final claim. The reason for using the t-test here and not the z-test is because of the number of observations. Since, we have three observations for each category; we will use the t-test. We will use the mean, minimum, and maximum observations. This will help us in making a claim if the two factors are linked or not.
The null hypothesis of the problem can be that the number of injuries per 100 workers increase with the number of hours worked. The alternative hypothesis of the situation can be that number of injuries per 100 workers do not vary with the number of hours worked. It can represented in the equation form below:
Number of Injuries per 100 workers increase with the number of hours worked
Ha: Number of Injuries per 100 workers do not vary with the number of hours worked
The significance level used in the test wills 95%. The t value of significance is 0.025 or more. (University of Regina, 2014)
The data interpretation gives us that the correlation between the two categories is 0.952948947 (Wuensch, 2014). Since we know that the ideal correlation is one, we are going to assume the idealist correlation as 1. This will give us the t-score of (0.95-1)/sqrt(1/3). The t-score tells us that the significance region is greater than -0.081494814 or less. Since, this region is not going to intersect or fall in the same region as the significance score, we can make a claim and can be 95% sure about the fact that the number of injuries do not increase with the number of hours worked. Hence, the analysis of the data is important in find a fact from the information and the raw data provided. It has helped us in proving a fact that we previously unknown. The claim is valid because it has gone through a series of statistical test, and can be proved using the statistic methods.
References
Wuensch, K. (2014). Comparing Coorelation Coefficient. Retrieved 26 November 2014, from http://core.ecu.edu/psyc/wuenschk/docs30/CompareCorrCoeff.pdfhttp://core.ecu.edu/psyc/wuenschk/docs30/CompareCorrCoeff.pdf
