The CEO of ABC manufacturing commissioned a study to look at the differences between the current salaries of her employees by employee job title. There were three job categories: clerical, custodial, and managerial. The study collected current salary data of the three groups and the researcher conducted a statistic and the results are presented below. Using the five STEPS of hypothesis testing, explain what the researcher might have done, including the appropriate analysis, and interpret the results. Are there any problems with this study? If so, explain what they are.
Average Salary
Clerical (n = 363) $27,838.54
Custodial (n = 27) $30,938.89
Manager (n = 84) $63,977.80
Test statistic = 434.48, p< .05
I know that the null is going to be rejected because the p value is less than the alpha, but how do I actually work the problem
To answer this question, let's go through the five steps of hypothesis testing:
Step 1: Formulate the Null and Alternative Hypotheses
The null hypothesis (H0) in this study would be that there is no significant difference in the salaries of employees across the job categories. The alternative hypothesis (H1) would suggest that there is a significant difference.
Step 2: Determine the Test Statistic and Significance Level
The given information provides the average salaries for each job category and the test statistic. The test statistic is not specified, but it is likely an F-statistic or a T-statistic, depending on the type of analysis performed. The significance level is mentioned as p < .05, which means that the researcher used a 5% level of significance.
Step 3: Conduct the Analysis
Without knowing the specific statistical analysis used, we can assume that the researcher performed an analysis of variance (ANOVA) or a t-test to compare the means of the three job categories.
Step 4: Evaluate the Results
The researcher obtained a test statistic of 434.48, and the p-value associated with this test statistic is less than 0.05 (p < .05). Since the p-value is less than the significance level, we can reject the null hypothesis and conclude that there is a significant difference in salaries across the job categories.
Step 5: Interpret the Results
Based on the analysis, there is evidence to suggest that there are significant differences in salaries among clerical, custodial, and managerial job categories in ABC manufacturing. The average salary for managers is significantly higher than both clerical and custodial employees, while the average salary for custodial employees is higher than clerical employees.
Problems with the Study:
1. Sample Size: The sample sizes for custodial (n=27) and managerial (n=84) job categories are relatively small compared to the clerical category (n=363). This could affect the statistical power and reliability of the results.
2. Missing Context: The study does not provide any additional information about the employees' qualifications, experience, or other relevant factors that could influence salary differences. Therefore, it is difficult to draw definitive conclusions about the causes of the observed salary disparities.
3. Non-Random Sampling: The sample may not represent the entire workforce of ABC manufacturing, and the method of employee selection is unclear. If the sample is not representative or the sampling method is biased, the findings may not generalize to the entire population.
4. Lack of Control Variables: The study only considers job title as the differentiating factor. However, other variables such as education, experience, or work performance could also contribute to salary differences. Not accounting for these variables may lead to misleading results.
5. Absence of Post-hoc Tests: While the study detects a significant difference between job categories, it does not provide any post-hoc tests or further analysis to determine specific pairwise differences between the categories. Additional post-hoc tests would be necessary to identify which specific groups differ significantly from each other.
It is important to consider these limitations when interpreting the study's findings and making any decisions based on them.