What is a proper Null and Alternative HypothesThe 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. (See grading rubric for additional paper requirements).
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
is for the following scenerio:
To properly analyze this scenario using the five steps of hypothesis testing, the researcher would have done the following:
Step 1: State the null and alternative hypotheses.
The null hypothesis (H0) is a statement of no effect or no difference between groups, while the alternative hypothesis (Ha) is the statement that contradicts the null hypothesis and suggests a significant difference or effect exists.
In this case, the null hypothesis would be that there is no significant difference in the average salaries among the three job categories (clerical, custodial, and managerial). The alternative hypothesis would be that there is a significant difference in the average salaries among the three job categories.
Step 2: Choose the appropriate statistical analysis.
Since we are comparing the average salaries of the three job categories, an appropriate statistical analysis to use would be Analysis of Variance (ANOVA). ANOVA allows for testing the hypotheses of equality of means across multiple groups.
Step 3: Set the significance level.
The significance level, denoted as α (alpha), is the probability of rejecting the null hypothesis when it is true. In this case, the statement "p < .05" indicates that the significance level is set to 0.05 or 5%.
Step 4: Conduct the statistical analysis and calculate the test statistic.
Using ANOVA, the researcher would calculate the test statistic to determine whether there is a significant difference in the average salaries among the three job categories. The test statistic value given as "434.48" is not typical for an ANOVA result, so it is unclear how this value was derived. Normally, ANOVA results would provide F-statistic, degrees of freedom, and p-value.
Step 5: Interpret the results and make a conclusion.
Without the proper test statistic value, it is difficult to interpret the results accurately or make a conclusion. In a typical ANOVA analysis, if the p-value is less than the significance level (e.g., p < .05), it would suggest evidence to reject the null hypothesis and conclude that there is a significant difference in the average salaries among the job categories.
Problems with this study:
1. Ambiguous test statistic: The given test statistic value (434.48) does not match with a typical ANOVA analysis, making it difficult to understand how this value was obtained. It is essential to provide accurate information in order to interpret the results correctly.
2. Sample size differences: The number of observations (n) in each job category is vastly different, with 363 for clerical, 27 for custodial, and 84 for managerial. This could potentially affect the power of the statistical analysis and the accuracy of the results. It is advisable to have a more balanced sample size across the groups.
3. Lack of information on data collection and methodology: The description of the study does not provide any details on how the salary data was collected or the precise statistical analysis applied. Without this information, it is challenging to assess the study's validity and potential biases.
4. Assumptions of ANOVA: ANOVA assumes that the data meets certain assumptions, such as normality and equal variances, which should be checked before conducting the analysis. Without information on these assumptions, it is unclear if they were met.
5. External validity: The study appears to be focused on the specific organization (ABC manufacturing), which may limit the generalizability of the findings to other companies or industries.