by | Jun 11, 2022 | APA 7th edition, Mathematics - Statistics
A) Linear Programming is used in all types of organizations in order to solve a wide variety of problems. Understanding the types of problems, and how LP problems can be modeled in Excel, and how optimal solutions can be found using Excels Solver add-in, are powerful methods of quantitative analysis. Typically, most of our efforts go into the development of the model. Develop a model for the following scenario which maximizes company profit and display this graphically. Use SolverTable to monitor the decision variables and the total profit.
Problem:
An electric vehicle company manufactures electric cars and SUVs. The amount of nickel used per vehicle is a strong contributor toward the development of electric vehicles and is being taken into effect as the main contributor used to maximize profit. Other materials are involved but this problem will focus on nickel alone.
Each electric SUV uses 40 ounces of nickel and produces $4,000 profit. Each electric car uses 30 ounces of nickel and produces $2,500 in profit. Marketing restrictions require that the number of cars produced must be at least twice the number of SUVs produced. There is 20,000 ounces of nickel available. A conversion of ounces to pounds can be performed in the tabulated results if necessary.
40 ounces = 2.5 pounds
30 ounces = 1.875 pounds.
20,000 ounces = 1,250 pounds
- Maximize the companys profit using Solver.
- Represent the data visually in order to show the maximized company profit.
- Use SolverTable to show what happens to the decision variables and the total profit when the availability of nickel varies from 10,000 to 30,000 in 1,000 ounce increments. How many extra ounces of nickel would the company be willing to pay for over its current 20,000 ounces? How much profit would the company lose if it lost any of its current 20,000 ounces?
B) In any optimization model such as those in this chapter, we say that the model is unbounded (and Solver will indicate as such) if there is no limit to the value of the objective. For example, if the objective is profit, then for any dollar value, no matter how large, a feasible solution exists with a profit at least this large. In the real world, why are there never any unbounded models? If you run Solver on a model and get an unbounded message, what should you do?
Using a graphic organizer of your choice, create a visual graphic that explains your answers to the questions above. Then, post your graphic organizer as an attachment. Use your creativity to make it appealing and clear enough for your classmates to understand, and reflect and comment upon.
by | Jun 11, 2022 | APA 7th edition, Mathematics - Statistics
Often in my unit we attempt to use other methods of pain relief for our patients. We have the option of using essential oils to help alleviate stress, pain, and anxiety in our patients. We learned in the lesson for this week that confidence intervals create a range wherein test results can be expected (Chamberlain, 2022). We use pharmacological interventions to help reduce anxiety and pain many times in the hospital, but what about non-pharmacological interventions like essential oils and aromatherapy? According to a study done on older adults with chronic pain, 82 participants were studied, if 44 participants had positive results due to aromatherapy (Tang,2014). This is what my excel spreadsheet would look like below.
This shows that with 95% confidence I can say that between 43% and 64% of the participants in the study showed results of having aromatherapy decrease pain. I used the proportion due to my sample size being so small.
Chamberlain University College of Nursing. (2022). MATH225: Statistical Reasoning for the Health Sciences, Week 6 Lesson: Confidence Intervals for Mean (Population Standard Deviation Known). (Online lesson). Downers Grove, IL.
Tang, S. K., & Tse, M. Y. M. (2014). Aromatherapy: Does it help to relieve pain, depression, anxiety, and stress in community-dwelling older persons? BioMed research international. Retrieved June 9, 2022, from https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4119713/.
by | Jun 7, 2022 | APA 7th edition, Mathematics - Statistics
Competency
Evaluate hypothesis tests for population parameters from one population.
Instructions
Scenario (information repeated for deliverable 01, 03, and 04)
A major client of your company is interested in the salary distributions of jobs in the state of Minnesota that range from $30,000 to $200,000 per year. As a Business Analyst, your boss asks you to research and analyze the salary distributions. You are given a spreadsheet that contains the following information:
- A listing of the jobs by title
- The salary (in dollars) for each job
Deliverable 4 – Hypothesis Tests.xlsx
In prior engagements, you have already explained to your client about the basic statistics and discussed the importance of constructing confidence intervals for the population mean. Your client says that he remembers a little bit about hypothesis testing, but he is a little fuzzy. He asks you to give him the full explanation of all steps in hypothesis testing and wants your conclusion about two claims concerning the average salary for all jobs in the state of Minnesota.
Background information on the Data
The data set in the spreadsheet consists of 364 records that you will be analyzing from the Bureau of Labor Statistics. The data set contains a listing of several jobs titles with yearly salaries ranging from approximately $30,000 to $200,000 for the state of Minnesota.
What to Submit
Your boss wants you to submit the spreadsheet with the completed calculations, answers, and analysis.
by | Jun 7, 2022 | APA 7th edition, Mathematics - Statistics
Develop a confidence interval for a population parameter.
Instructions
Scenario (information repeated for deliverable 01, 03, and 04)
A major client of your company is interested in the salary distributions of jobs in the state of Minnesota that range from $30,000 to $200,000 per year. As a Business Analyst, your boss asks you to research and analyze the salary distributions. You are given a spreadsheet that contains the following information:
- A listing of the jobs by title
- The salary (in dollars) for each job
Deliverable 3 – Confidence Intervals.xlsx
You have previously explained some of the basic statistics to your client already, and he really liked your work. Now he wants you to analyze the confidence intervals.
Background information on the Data
The data set in the spreadsheet consists of 364 records that you will be analyzing from the Bureau of Labor Statistics. The data set contains a listing of several jobs titles with yearly salaries ranging from approximately $30,000 to $200,000 for the state of Minnesota.
What to Submit
Your boss wants you to submit the spreadsheet with the completed calculations, answers, and analysis.
by | Jun 7, 2022 | APA 7th edition, Mathematics - Statistics
Apply the normal distribution, standard normal distribution, and central limit theorem.
Scenario
Frank has only had a brief introduction to statistics when he was in high school 12 years ago, and that did not cover inferential statistics. He is not confident in his ability to answer some of the problems posed in the course.
As Frank’s tutor, you need to provide Frank with guidance and instruction on a spreadsheet he has partially filled out. Your job is to help him understand and comprehend the material. You should not simply be providing him with an answer as this will not help when it comes time to take the test. Instead, you will be providing a step-by-step breakdown of the problems including an explanation on why you did each step and using proper terminology.
What to Submit
To complete this assignment, you must first download the spreadsheet, and then complete it by including the following items on the spreadsheet:
Deliverable 2 – Tutoring on the Normal Distribution_.xlsx
- Incorrect Answers – Correct any wrong answers. You must also explain the error performed in the problem in your own words.
- Partially Finished Work – Complete any partially completed work. Make sure to provide step-by-step instructions including explanations.
- Blank Questions – Show how to complete any blank questions by providing step-by-step instructions including explanations.
Your step-by-step breakdown of the problems, including explanations and calculations performed, should be present within the Excel spreadsheet provided.
by | Jun 7, 2022 | APA 7th edition, Mathematics - Statistics
In everyday terms, a confidence interval is the range of values around a sample statistic (such as mean or proportion) within which clinicians can expect to get the same results if they repeat the study protocol or intervention, including measuring the same outcomes the same ways. As you ask yourself, “Will I get the same results if I use this research?”, you must address the precision of study findings, which is determined by the Confidence Interval. If the CI around the sample statistic is narrow, you can be confident you will get close to the same results if you implement the same research in your practice.
Consider the following example. Suppose that you did a systematic review of studies on the effect of tai chi exercise on sleep quality, and you found that tai chi affected sleep quality in older people. If, according to your study, you found the lower boundary of the CI to be .49, the study statistic to be 0.87, and the upper boundary to be 1.25, this would mean that each end limit is 0.38 from the sample statistic, which is a relatively narrow CI.
(UB + LB)/2 = Statistic [(1.25 + .49)/2 = .87]
Keep in mind that a mean difference of 0 indicates there is no difference; this CI does not contain 0. Therefore, the sample statistic is statistically significant and unlikely to occur by chance.
Because this was a systematic review, and tai chi exercise has been established from the studies you assessed as helping people sleep, based on the sample statistics and the CI, clinicians could now use your study and confidently include tai chi exercises among possible recommendations for patients who have difficulty sleeping.
Now you can apply your knowledge of CIs to create your own studies and make wise decisions about whether to base your patient care on a particular research finding.
Initial Post Instructions
Thinking of the many variables tracked by hospitals and doctors’ offices, confidence intervals could be created for population parameters (such as means or proportions) that were calculated from many of them. Choose a topic of study that is tracked (or that you would like to see tracked) from your place of work. Discuss the variable and parameter (mean or proportion) you chose, and explain why you would use these to create an interval that captures the true value of the parameter of patients with 95% confidence.
Consider the following:
How would changing the confidence interval to 90% or 99% affect the study? Which of these values (90%, 95%, or 99%) would best suit the confidence level according to the type of study chosen? How might the study findings be presented to those in charge in an attempt to affect change at the workplace
