The testing of the claim that the difference in annual bonuses is higher than $100 at the 0.05 level of significance requires four steps: formulation of the hypothesis, data collection, data analysis, and reporting. The formulation of the hypothesis involves the formulating the null-hypothesis and the alternate-hypothesis. The null hypothesis is the opposite of the claim. As such, the average difference in annual bonuses between company A and company B is equal to $100 at a 0.05 level of significance. The alternate hypothesis on the other hand will be upper-tailed. It states that the average difference between the annual bonuses between company A and company B is greater than $100 at a 0.05 level of significance.
The next step is the collection of data. Data collected bases on the research design. In this instance, we choose an experimental design. It requires the collection of data on the annual bonus from a representative sample of employees of company A and Company B.
Delegate your assignment to our experts and they will do the rest.
Statistical techniques are then used to analyze the collected data. The analysis starts by calculating the statistical characteristics of the data that include the means of the samples, the mean of the differences in annual bonuses, the standard deviation of the differences, and sample size. The data is then subjected to a one-tailed t-test. In the test, the mean difference of the annual bonuses is compared to a fixed value of $100. A t-test requires the calculation of the test statistic, a value that provides a summary characteristic of the dataset. The test statistics give the critical value that is obtained from the t-test statistical distribution table. The null-hypothesis accepted if test statistics fall in the acceptance region. Otherwise, it is rejected, and the alternate hypothesis assumed.
Finally, the data is reported through a report that comprises literature, figure, graphs, and tables. The reports provide a summary of the claim, data used, size of the sample, and the finding. It should also conclude by providing an interpretation of the findings.
