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 hypothesis testing with one sample.
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. She intends 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:
- Null hypothesis
- Alternative hypothesis
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 it here.
- Random variable: Explain what a random variable is. Locate it in the assignment description, and enter it 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.
Title of the Document
Student’s Name
American Intercontinental University
Running head: STUDENT’S TOPIC
STUDENT’S RESEARCH TOPIC 4
Abstract:
[(Don’t Indent) In 150 words or less, summarize your Breadth paper. What is the paper about and explain your conclusion?]
Introduction
[Explanation : In this section, describe what will be discussed in this report. Briefly describe all main components. Main requirements can be found in assignment description or in this template as separate sections under specific titles. Please DELETE explanations and replace with project-specific text.]
Scenario Analysis
[Explanation : Please read a scenario in the assignment description section and answer the following questions in a substantive manner. Please justify your recommendations. It is important that you elaborate your answer rather than providing one or two words answers. Please DELETE explanations and replace with project-specific text.]
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? Explain your choice thoroughly.
State both hypotheses:
Null hypothesis:
Alternative hypothesis:
Define the following:
1. Standard deviation: Explain what standard deviation is. What is the standard deviation of the sample provided?
2. Random variable: Explain what a random variable is and where in the assignment description you can find it. Describe the random variable.
3. Test type: Compare and contrast t-tests and z-tests. What is the main difference between the two tests? Once done, determine which is appropriate in this 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 assignment description is high, medium, or low. What are some scenarios where you would want a very low level of significance? Locate the level of significance in the assignment description, and list it in this step.
Define the following:
1. Degrees of freedom: Explain what degrees of freedom care. What is the equation for calculating the degrees of freedom? Determine the degree of freedom based on the number of reviewed documents in the new experiment.
2. Critical value: Explain what the critical value is and how you can determine it. Find the critical value by using a 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 statistic based on the test type determined in Step 1 and calculate the test statistics. If the determination was done correctly, you should use this formula: .
STEP 4: COMPARE THE CALCULATED TEST STATISTICS AND THE CRITICAL VALUE
Construct a bell-shaped diagram based on this problem. Explain what it means for the test statistic to be in the “rejection region. Does our test statistic fall within the rejection region?
Insert bell-shaped diagram showing critical value and calculated test statistic:
Conclusion
[ Articulate a conclusion regarding your hypothesis testing. Should we reject or fail to reject our null hypothesis? Elaborate within the context of this problem]
References
Double space does not indent but do alphabetize. Use APA style. If the citation carries over to the next line, the lines will automatically be in hanging indent when you use the following template (overwrite the first two and when you hit <enter> twice after that, the references will fall in hanging indent naturally).
Applebaum, B. C., Zuckerman, M. Y., & Wu, X. (2014). Title of article in sentence case: Subtitle in sentence case. Journal in Title Case, X, 45-56.
O’Hara, C. (1986). Name of book in sentence case: Subtitle in sentence case. City, ST: Name of Publisher.
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