Analysis of Staffing Needs for the Foreclosure Department
What is the purpose of the hypothesis testing in this scenario?
Purpose of Hypothesis Testing:
The purpose of the hypothesis testing in this scenario is to determine whether the introduction of a larger monitor has a significant impact on reducing the processing time for reviewing foreclosure documents in the Foreclosure Department. Hypothesis testing helps in evaluating the validity of the manager's claim that providing a larger monitor can lead to a shorter processing time.
Analysis of the Hypothesis Testing Process:
Step 1: Set Up Null and Alternative Hypotheses
In hypothesis testing, we define the null hypothesis (H0) and the alternative hypothesis (Ha) to test the claim or assumption. In this scenario:
Null Hypothesis (H0): The larger monitor does not have any effect on the processing time for reviewing foreclosure documents.
Alternative Hypothesis (Ha): The larger monitor does have an effect on the processing time for reviewing foreclosure documents.
Step 2: Decide the Level of Significance
The significance level (α) is set at 0.05, indicating a 95% confidence level. This level determines the probability of making a Type I error, which is the chance of incorrectly rejecting the null hypothesis when it is true. The degree of freedom (df) is calculated as n - 1, resulting in 19 in this case.
Step 3: Calculate the Test Statistics
With a sample size less than 30, a t-test is appropriate. The test statistics formula is applied to compare the sample mean, population mean, sample standard deviation, and sample size to determine the effect of a larger monitor on processing time.
Step 4: Compare the Calculated Test Statistics and the Critical Value
A bell-shaped diagram is constructed to compare the critical value with the calculated test statistics. This helps in visualizing whether the effect of the larger monitor falls within the critical region for significance.
Step 5: Reach a Conclusion
By comparing the calculated test statistics with the critical value, a conclusion is drawn regarding the rejection or acceptance of the null hypothesis. This step determines whether the manager's claim about the impact of a larger monitor on processing time is supported by statistical analysis.