Category: Statistics

Answer all questions except question 2,3, and 4.
Please read instructions carefully and answer the questions correctly.
Let me know if any files don’t open.
Thanks.

Here are the details:
Initial Post : For your initial post, you should choose and solve one of the problems from the document posted above. To do so, please try to print out the single page, solve the problem, scan back in and post. You may also just state the number of the problem and solve it in the discussion itself using the math typesetting if you would like. You should try to choose a problem that people haven’t done yet or use a different technique if you solve one that has already been posted. Make sure to post the problem number in the subject line of your post.
Be sure to explain HOW how you solved it. Did you use the calculator? a Table? StatCrunch? Really explain it so others can understand! 🙂
If you’d like, you may post a video of you solving it!
Follow-up Posts: You are required to post AT LEAST 2 follow-up posts. These can be replies to other students, additional solved review problems, videos or website resources that have helped you study, etc. If someone has already replied, please make sure to make your reply unique by offering another suggestion, a different place to look, or comment on someone else’s question.
You are more than welcome to solve more problems!

This is a written discussion board assignment, so please respond to the following prompt in an essay response of around 150 words.
Prompt: For this discussion board post, explain the following three things:
What are degrees of freedom?
Why do we divide SS by df instead of by N when estimate population variance?
What is the difference between a one-sample t-test and a dependent samples t-test

Competency
In this project, you will demonstrate your mastery of the following competency:
Apply statistical techniques to address research problems
Perform hypothesis testing to address an authentic problem
Overview
In this project, you will apply inference methods for means to test your hypotheses about the housing sales market for a region of the United States. You will use appropriate sampling and statistical methods.
Scenario
You have been hired by your regional real estate company to determine if your region’s housing prices and housing square footage are significantly different from those of the national market. The regional sales director has three questions that they want to see addressed in the report:
Are housing prices in your regional market lower than the national market average?
Is the square footage for homes in your region different than the average square footage for homes in the national market?
For your region, what is the range of values for the 95% confidence interval of square footage for homes in your market?
You are given a real estate data set that has houses listed for every county in the United States. In addition, you have been given national statistics and graphs that show the national averages for housing prices and square footage. Your job is to analyze the data, complete the statistical analyses, and provide a report to the regional sales director. You will do so by completing the Project Two Template located in the What to Submit area below.
Directions
Introduction
Region: Start by picking one region from the following list of regions:
West South Central, West North Central, East South Central, East North Central, Mid Atlantic
Purpose: What is the purpose of your analysis?
Sample: Define your sample. Take a random sample of 500 house sales for your region.
Describe what is included in your sample (i.e., states, region, years or months).
Questions and type of test: For your selected sample, define two hypothesis questions (see the Scenario above) and the appropriate type of test for each. Address the following for each hypothesis:
Describe the population parameter for the variable you are analyzing.
Describe your hypothesis in your own words.
Identify the hypothesis test you will use (1-Tail or 2-Tail).
Level of confidence: Discuss how you will use estimation and confidence intervals to help you solve the problem
1-Tail Test
Hypothesis: Define your hypothesis.
Define the population parameter.
Write null (Ho) and alternative (Ha) hypotheses. Note: For means, define a hypothesis that is less than the population parameter.
Specify your significance level.
Data analysis: Summarize your sample data using appropriate graphical displays and summary statistics and confirm assumptions have not been violated to complete this hypothesis test.
Provide at least one histogram of your sample data.
In a table, provide summary statistics including sample size, mean, median, and standard deviation. Note: For quartiles 1 and 3, use the quartile function in Excel:
=QUARTILE([data range], [quartile number])
Summarize your sample data, describing the center, spread, and shape in comparison to the national information (under Supporting Materials, see the National Summary Statistics and Graphs House Listing Price by Region PDF). Note: For shape, think about the distribution: skewed or symmetric.
Check the conditions.
Determine if the normal condition has been met.
Determine if there are any other conditions that you should check and whether they have been met. Note: Think about the central limit theorem and sampling methods.
Hypothesis test calculations: Complete hypothesis test calculations.
Calculate the hypothesis statistics.
Determine the appropriate test statistic (t). Note: This calculation is (mean – target)/standard error. In this case, the mean is your regional mean, and the target is the national mean.
Calculate the probability (p value). Note: This calculation is done with the T.DIST function in Excel:
=T.DIST([test statistic], [degree of freedom], True) The degree of freedom is calculated by subtracting 1 from your sample size.
Interpretation: Interpret your hypothesis test results using the p value method to reject or not reject the null hypothesis.
Relate the p value and significance level.
Make the correct decision (reject or fail to reject).
Provide a conclusion in the context of your hypothesis.
2-Tail Test
Hypotheses: Define your hypothesis.
Define the population parameter.
Write null and alternative hypotheses. Note: For means, define a hypothesis that is not equal to the population parameter.
State your significance level.
Data analysis: Summarize your sample data using appropriate graphical displays and summary statistics and confirm assumptions have not been violated to complete this hypothesis test.
Provide at least one histogram of your sample data.
In a table, provide summary statistics including sample size, mean, median, and standard deviation. Note: For quartiles 1 and 3, use the quartile function in Excel:
=QUARTILE([data range], [quartile number])
Summarize your sample data, describing the center, spread, and shape in comparison to the national information. Note: For shape, think about the distribution: skewed or symmetric.
Check the assumptions.
Determine if the normal condition has been met.
Determine if there are any other conditions that should be checked on and whether they have been met. Note: Think about the central limit theorem and sampling methods.
Hypothesis test calculations: Complete hypothesis test calculations.
Calculate the hypothesis statistics.
Determine the appropriate test statistic (t). Note: This calculation is (mean – target)/standard error. In this case, the mean is your regional mean, and the target is the national mean.]
Determine the probability (p value). Note: This calculation is done with the TDIST.2T function in Excel:
=T.DIST.2T([test statistic], [degree of freedom]) The degree of freedom is calculated by subtracting 1 from your sample size.
Interpretation: Interpret your hypothesis test results using the p value method to reject or not reject the null hypothesis.
Compare the p value and significance level.
Make the correct decision (reject or fail to reject).
Provide a conclusion in the context of your hypothesis.
Comparison of the test results: Revisit Question 3 from the Scenario section: For your region, what is the range of values for the 95% confidence interval of square footage for homes?
Calculate and report the 95% confidence interval. Show or describe your method of calculation.
Final Conclusions
Summarize your findings: In one paragraph, summarize your findings in clear and concise plain language.
Discuss: Discuss whether you were surprised by the findings. Why or why not?

Textbook: Tokunaga, H. (2019). Fundamental Statistics for the Social and Behavioral Sciences (2nd ed.). Thousand Oaks, CA: Sage Publications, Inc
Complete and discuss your finding for exercise number 12 and exercise number 18 in your textbook. They are at the end of chapter 4, listed under 4.15 Exercises, on page 111 in the textbook. 
#12 – 50 points
#18 – 50 points

In real-life applications, statistics helps us analyze data to extract information about a population. In this module discussion, you will take on the role of Susan, a high school principal. She is planning on having a large movie night for the high school. She has received a lot of feedback on which movie to show and sees differences in movie preferences by gender and also by grade level.
She knows if the wrong movie is shown, it could reduce event turnout by 50%. She would like to maximize the number of students who attend and would like to select a PG-rated movie based on the overall student population’s movie preferences. Each student is assigned a classroom with other students in their grade. She has a spreadsheet that lists the names of each student, their classroom, and their grade. Susan knows a simple random sample would provide a good representation of the population of students at their high school, but wonders if a different method would be better.
You can review the student demographics here: Module One Discussion Data PDF.
In your initial discussion post, specifically address the following:
Introduce yourself and describe a time when you used data in a personal or professional decision. This could be anything from analyzing sales data on the job to making an informed purchasing decision about a home or car.
Describe to Susan how to take a sample of the student population that would not represent the population well.
Describe to Susan how to take a sample of the student population that would represent the population well.
Finally, describe the relationship of a sample to a population and classify your two samples as random, systematic, cluster, stratified, or convenience.

Minimum of 1 scholarly source AND one appropriate resource such as the textbook, math video and/or math website
In your reference for this assignment, be sure to include both your text/class materials AND your outside reading(s).
Initial Post Instructions
Describe a hypothesis test study that would help your work or conclusions in some way. Describe what variable would be tested and what would be your guess of the value of that variable. Then include how the result, if the null were rejected or not, might change your conclusions or actions in some way.

The purpose of this assignment is to apply a waiting line model to a business service operation in order to recommend the most efficient use of time and resources.
(This assignment has been adapted from Case Problem 2 in Chapter 15 of the textbook.)
Use the information in the scenario provided to prepare a managerial report for Office Equipment, Inc. (OEI). 
Scenario
Office Equipment, Inc. (OEI) leases automatic mailing machines to business customers in Fort Wayne, Indiana. The company built its success on a reputation of providing timely maintenance and repair service. Each OEI service contract states that a service technician will arrive at a customer’s business site within an average of 3 hours from the time that the customer notifies OEI of an equipment problem.
Currently, OEI has 10 customers with service contracts. One service technician is responsible for handling all service calls. A statistical analysis of historical service records indicates that a customer requests a service call at an average rate of one call per 50 hours of operation. If the service technician is available when a customer calls for service, it takes the technician an average of 1 hour of travel time to reach the customer’s office and an average of 1.5 hours to complete the repair service. However, if the service technician is busy with another customer when a new customer calls for service, the technician completes the current service call and any other waiting service calls before responding to the new service call. In such cases, after the technician is free from all existing service commitments, the technician takes an average of 1 hour of travel time to reach the new customer’s office and an average of 1.5 hours to complete the repair service. The cost of the service technician is $80 per hour. The downtime cost (wait time and service time) for customers is $100 per hour.
OEI is planning to expand its business. Within 1 year, OEI projects that it will have 20 customers, and within 2 years, OEI projects that it will have 30 customers. Although OEI is satisfied that one service technician can handle the 10 existing customers, management is concerned about the ability of one technician to meet the average 3-hour service call guarantee when the OEI customer base expands. In a recent planning meeting, the marketing manager made a proposal to add a second service technician when OEI reaches 20 customers and to add a third service technician when OEI reaches 30 customers. Before making a final decision, management would like an analysis of OEI service capabilities. OEI is particularly interested in meeting the average 3-hour waiting time guarantee at the lowest possible total cost.
Managerial Report
Develop a managerial report (1,000-1,250 words) summarizing your analysis of the OEI service capabilities. Make recommendations regarding the number of technicians to be used when OEI reaches 20 and then 30 customers, and justify your response. Include a discussion of the following issues in your report:
What is the arrival rate for each customer?
What is the service rate in terms of the number of customers per hour? (Remember that the average travel time of 1 hour is counted as service time because the time that the service technician is busy handling a service call includes the travel time in addition to the time required to complete the repair.)
Waiting line models generally assume that the arriving customers are in the same location as the service facility. Consider how OEI is different in this regard, given that a service technician travels an average of 1 hour to reach each customer. How should the travel time and the waiting time predicted by the waiting line model be combined to determine the total customer waiting time? Explain.
OEI is satisfied that one service technician can handle the 10 existing customers. Use a waiting line model to determine the following information: (a) probability that no customers are in the system, (b) average number of customers in the waiting line, (c) average number of customers in the system, (d) average time a customer waits until the service technician arrives, (e) average time a customer waits until the machine is back in operation, (f) probability that a customer will have to wait more than one hour for the service technician to arrive, and (g) the total cost per hour for the service operation.
Do you agree with OEI management that one technician can meet the average 3-hour service call guarantee? Why or why not?
What is your recommendation for the number of service technicians to hire when OEI expands to 20 customers? Use the information that you developed in Question 4 (above) to justify your answer.
What is your recommendation for the number of service technicians to hire when OEI expands to 30 customers? Use the information that you developed in Question 4 (above) to justify your answer.
What are the annual savings of your recommendation in Question 6 (above) compared to the planning committee’s proposal that 30 customers will require three service technicians? (Assume 250 days of operation per year.) How was this determination reached?

Instructions
Write a paper incorporating concepts that you learned during the course, using your survey results. You can start with your discussion post responses in Weeks 4 – 7 as a guide. Write a paper (about 2-3 written pages, 4-5 pages include graphs and results), double-spaced and in 12-point font. You will use Excel and/or StatCrunch for this project.
The final project paper will include:
A title
An Introduction
A paragraph on how you sampled the data. Share limitations in your sampling method and discuss the reliability of the survey responses.
Measures of central tendency and variation. Interpret the results in complete sentences. What do these results tell you about your data?
Three graphs with at least one that summarizes categorical data and one that summarizes numerical data. Include captions for each graph.
A confidence interval calculated using Excel or StatCrunch. Use a question from discussion post four and answer it using the confidence interval. Include the results and interpret the confidence interval. A hypothesis test including H0 and Ha answering a second question from discussion post four written as a claim. Include analysis showing the conditions are met, the test statistic and p-value, and a written conclusion. Include the results from StatCrunch. The body of the paper should be written around the results from your graphs, confidence interval and hypothesis test.
Conclusion (Think about what outcomes you found interesting or unexpected.)
Submitting Your Assignment to the Dropbox:
Submit a written paper including the above requirements
Submit a separate document with the survey questions.
Submit the Excel file with the raw data (original data with no calculations or graphs) collected from the survey.

I have included questions as attachments: It should be three questions
Complete exercises numbered 12, 18, and 20 in your textbook. They are at the end of chapter 2, listed under 2.12 Exercises, on page 45 in the textbook. 
Textbook: Tokunaga, H. (2019). Fundamental Statistics for the Social and Behavioral Sciences (2nd ed.). Thousand Oaks, CA: Sage Publications, Inc