The below scenario describes a real-world or business application that utilizes statistical analysis to help resolve a business problem: increasing efficiency by decreasing processing time. Prepare an analysis by completing five steps of the hypothesis testing with one sample. The report should be a minimum of 5 pages in length.
Last week, your manager asked you to analyze staffing needs for the Foreclosure Department. She was so impressed, and she wants you to create another report for her. Her intention is to decrease the processing time per document.
Based on last week’s report, the average number of processed documents per hour was 15.11, with a standard deviation of 2.666. That is, one document was reviewed in 238.25 seconds. To be objective as much as possible, the manager spoke with an employee whose average was exactly 15 documents per hour. The employee claimed that if she was given a larger monitor, the processing time would be shorter.
They conducted an experiment with a large monitor and measured processing time. After reviewing 20 documents, the calculated average processing time per document was 190.58 seconds. The manager believes that a bigger monitor helped reduce the processing time for reviewing foreclosure documents. Conduct a hypothesis test using a 95% confidence level, which means that significance level a = 0.05.
Use the 5-step process, and explain each term or concept mentioned in each section in the following.
Step 1: Set Up Null and Alternative Hypotheses
Based on the request description, explain if a one-tailed or two-tailed test is needed. If a one-tailed test is needed, is it a left or right-tailed test? Please explain why one alternative is better than the other.
State both of the following hypotheses:
You will need the following information to progress to Step 2:
Standard deviation: Explain what standard deviation is. Locate the calculated standard deviation in the assignment description, and enter here.
Random variable: Explain what a random variable is. Locate it in the assignment description, and enter here.
Test type: Compare and contrast t-test and z-test. Once done, determine which one is appropriate for the experiment given the fact that the sample size is less than 30.
Step 2: Decide the Level of Significance
Explain what the significance level is, and determine whether the one used in the assignment description is high, medium, or low. What does this significance level tell you about this test? Locate the level of significance in the given scenario, and list it in this step.
Significance level = ?
Determine the degree of freedom based on the number of reviewed documents in the new experiment (n = 20) and based on the formula Degree of freedom = n – 1.
Degree of freedom = ?
Critical value = (You will need to use the t-table and find the intersection point between the degree of freedom and the alpha value that is provided in the assignment description.)
Step 3: Calculate the Test Statistics
Calculate the test statistics based on the test type determined in Step 1.
If the determination was done correctly, you should use this formula to calculate the test statistics.
Test statistics = ?
Step 4: Compare the Calculated Test Statistics and the Critical Value
Construct a bell-shaped diagram showing the critical value and the calculated test statistic.
Step 5: Reach a Conclusion
Was the manager’s conclusion correct? Share your conclusions on the assumptions in the scenario using the hypothesis testing that you conducted in the previous four steps.