7/17/2016 Assessment 2 - MBAFP6018 Spring 2016 Section 01 ASSESSMENT 2 Estimating From Samples Details Attempt 1 Available Attempt 2 Attempt 3 Overview Use provided data files and scenarios to complete a confidence interval and to estimate a sample size. For both scenarios, create tables to demonstrate your methods and findings and write brief summaries (3-5 sentences) to communicate your results to relevant stakeholders. Note: The assessments in this course build upon each other, so you are strongly encouraged to complete them in sequence. Managers use hypothetical sampling distributions to make estimates about characteristics (parameters) of a population, based on measurements from a sample. This assessment allows you to apply inferential data analysis techniques to business decisions. By successfully completing this assessment, you will demonstrate your proficiency in the following course competencies and assessment criteria: Competency 1: Evaluate the quality and fit of data for use in business analysis. Create a table for examining data for use in business analysis. Competency 3: Analyze business decision opportunities using basic inferential statistics. Apply inferential data analysis techniques to develop a correct confidence interval. Apply inferential data analysis techniques to correctly estimate sample size. Competency 5: Apply data analysis to general business management planning and decision making. Compile findings into a management report with details for recommended actions. Competency 6: Communicate in a manner that is professional and consistent with expectations for members of the business professions. Communicate in a manner that is professional and consistent with expectations for members of the business professions. Competency Map Check Your ProgressUse this online tool to track your performance and progress through your course. Context Sampling is used when it is not feasible to survey an entire data population, such as when trying to determine how many people living in New York City drink Diet Coke. By using the proper statistical methods, you can sample the population to determine, within an established confidence level, a statistically valid number to answer your survey question. Questions to Consider To deepen your understanding, you are encouraged to consider the questions below and discuss them with a fellow learner, a work associate, an interested friend, or a member of the business community. https://courserooma.capella.edu/webapps/blackboard/content/listContent.jsp?course_id=_34646_1&content_id=_3445793_1&mode=reset 1/4 7/17/2016 Assessment 2 - MBAFP6018 Spring 2016 Section 01 The human resources (HR) manager for Gorman Industries, LLC wants to give a short survey to a sample of recent hires (defined as people who have been with the company for less than one year). This sample will include several thousand individuals. The HR manager wants to be able to develop a confidence interval for the proportion of new hires that are happy with the company. To get the sample, he has developed two alternative plans: Plan 1: Stand at the door as people are entering and leaving a quarterly employee communications meeting. Whenever he sees someone with a red badge, which indicates less than one year with the company, he will stop that person and give him or her a packet with the survey and instructions. Plan 2: Email new employees with the packet attached and request they complete it and email it back within three days. Which planned approach would you use, and why? Base your decision on statistical fact, potential cost, and HR management time needed to evaluate the results. Assume that a reasonable estimate for the proportion of new hires that are happy with the company is .8. Resources Required Resources The following resources are required to complete the assessment. Capella Resources Click the links provided to view the following resources: Area Gas Prices - Random Sample. Confidence Interval Calculator. Sample Size Estimator. Suggested Resources The following optional resources are provided to support you in completing the assessment or to provide a helpful context. For additional resources, refer to the Research Resources and Supplemental Resources in the left navigation menu of your courseroom. Capella Resources Capella University partners with Sophia Learning to provide tutorials and other learning resources online. For this assessment, you are encouraged to study the following Sophia tutorials: Fitz (Producer). (n.d.). Zscores [Video] | Transcript. Retrieved from http://www.sophia.org/zscores/zscores6 tutorial Varela, A. (Producer). (n.d.). Contrasting sampling methods [Video] | Transcript. Retrieved from http://www.sophia.org/contrastingsamplingmethods/contrastingsamplingmethods5tutorial Greene, A. (Producer). (n.d.). Standard error [Video] | Transcript. Retrieved from http://www.sophia.org/standarderrortutorial Capella Multimedia Click the links provided below to view the following multimedia pieces illustrating the use of the tools: Confidence Interval Calculator | Transcript. Sample Size Estimator | Transcript. Course Library Guide A Capella University library guide has been created specifically for your use in this course. You are encouraged to refer to the resources in the MBAFP6018 - Data Analysis for Business Decisions Library Guide to help direct your research. Internet Resources https://courserooma.capella.edu/webapps/blackboard/content/listContent.jsp?course_id=_34646_1&content_id=_3445793_1&mode=reset 2/4 7/17/2016 Assessment 2 - MBAFP6018 Spring 2016 Section 01 Internet Resources Access the following resources by clicking the links provided. Please note that URLs change frequently. Permissions for the following links have been either granted or deemed appropriate for educational use at the time of course publication. StatisticsLectures.com (Producer). (n.d.). Confidence intervals about the mean, population standard deviation known [Video] | Transcript. Retrieved from http://www.statisticslectures.com/topics/cimeanstandarddeviationknown/ StatisticsLectures.com (Producer). (n.d.). Confidence intervals about the mean, population standard deviation unknown [Video] | Transcript. Retrieved from http://www.statisticslectures.com/topics/cimeanstandarddeviationunknown/ StatisticsLectures.com (Producer). (n.d.). Confidence intervals for population proportions [Video] | Transcript. Retrieved from http://www.statisticslectures.com/topics/cipopulationproportions/ StatisticsLectures.com (Producer). (n.d.). Calculating required sample size to estimate population mean [Video] | Transcript. Retrieved from http://www.statisticslectures.com/topics/samplesizepopulationmean/ StatisticsLectures.com (Producer). (n.d.). Calculating required sample size to estimate population proportions [Video] | Transcript. Retrieved from http://www.statisticslectures.com/topics/samplesizepopulationproportion/ Bookstore Resources The resources listed below are relevant to the topics and assessments in this course and are not required. Unless noted otherwise, these materials are available for purchase from the Capella University Bookstore. When searching the bookstore, be sure to look for the Course ID with the specific -FP (FlexPath) course designation. Bowerman, B., O'Connell, R., & Murphree, E. (2014). Business statistics in practice (7th ed.). New York, NY: McGraw Hill. Salkind, N. J. (Ed.). (2013). Excel statistics: A quick guide (2nd ed.). Thousand Oaks, CA: Sage. Other Books The resources listed below are relevant to the topics and assessments in this course and are not required. You may wish to purchase the following optional books from your preferred bookseller: Slaughter, S. J., & Delwiche, L. D. (2010). The little SAS book for Enterprise Guide 4.2. Cary, NC: SAS Institute. Assessment Instructions Use the following files, linked in the Resources under the Required Resources heading, to complete both of the scenarios for this assessment: Confidence Interval Calculator. Area Gas Prices - Random Sample. Sample Size Estimator. Practical Application Scenario 1 To complete this scenario, use the Confidence Interval Calculator and the Area Gas Prices - Random Sample files. The Minneapolis Star Tribune newspaper has decided to write an article about gasoline prices in the Twin Cities area (Minneapolis and Saint Paul, Minnesota). The Star Tribune has designed a survey and taken a simple random sample of regular, unleaded gas prices at 70 area stations. The results are in the Area Gas Prices - Random Sample file. The Star Tribune's policy is that no data will be reported unless it is 95 percent confident that the numbers are correct. As the new manager of the data verification unit at the Star Tribune, you need to develop a 95 percent confidence interval for the average price of regular unleaded gasoline in the area. Complete a confidence interval for the data provided, using tables to demonstrate your method and findings. https://courserooma.capella.edu/webapps/blackboard/content/listContent.jsp?course_id=_34646_1&content_id=_3445793_1&mode=reset 3/4 7/17/2016 Assessment 2 - MBAFP6018 Spring 2016 Section 01 Write a 3-5 sentence summary that communicates your results to the Star Tribune's business manager. Practical Application Scenario 2 To complete this scenario, use the Sample Size Estimator file. The third shift at Microsoft Windows' security unit in Redmond, Washington, is considering replacing its coffee brewing units with new Germanmade brewers. As the newest member of this elite Microsoft team, you have been assigned to investigate this proposal. Develop a 99 percent confidence interval for the average yield (cups per pound) for the new German coffee brewer. The margin of error should be no bigger than .3 (three tenths of a cup). Based on experience with the current coffee makers, your best guess for the population standard deviation, sigma, is 1.2 cups. How large a sample do you need? Calculate the estimated sample size needed for the above scenario, using tables to demonstrate your method and findings. Write a 3-5 sentence summary that communicates your results to the business manager. Additional Requirements Compile your work for both scenarios in one Microsoft Word file: Paste in the tables you used. Clearly title your tables, including each row and column. Highlight the results of your data calculations within each table. Summarize your findings for each scenario in a 3-5 sentence paragraph below each table. Estimating From Samples Scoring Guide View Scoring Guide Use the scoring guide to enhance your learning. How to use the scoring guide [U02a1] Estimating From Samples Use provided data files and scenarios to complete a confidence interval and to estimate a sample size. For both scenarios, create tables to demonstrate your methods and findings and write brief summaries (3-5 sentences) to communicate your results to relevant stakeholders. Submit Assessment This button will take you to the next available assessment attempt tab, where you will be able to submit your assessment. U02a1: Estimating From Samples >> View/Complete U02a1: Estimating From Samples: Revision 1 >> View/Complete U02a1: Estimating From Samples: Revision 2 >> View/Complete https://courserooma.capella.edu/webapps/blackboard/content/listContent.jsp?course_id=_34646_1&content_id=_3445793_1&mode=reset 4/4 Area Gas Prices - Random Sample Minneapolis Price of Regular Station Unleaded 1 $3.24 2 $3.03 3 $3.63 4 $3.58 5 $2.94 6 $3.68 7 $3.14 8 $3.36 9 $3.40 10 $3.20 11 $2.85 12 $3.80 13 $3.31 14 $3.78 15 $3.43 16 $3.27 17 $3.18 18 $3.48 19 $3.00 20 $3.36 21 $3.52 22 $3.26 23 $3.04 24 $3.17 25 $3.26 26 $3.27 27 $3.30 28 $3.51 29 $3.80 30 $3.05 31 $3.56 32 $3.53 33 $2.96 34 $3.57 35 $3.58 End of worksheet Station 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 St. Paul Price of Regular Unleaded $3.05 $2.89 $3.84 $3.50 $2.78 $3.51 $3.33 $3.31 $3.20 $3.15 $2.75 $3.79 $3.10 $3.92 $3.31 $3.45 $3.17 $3.44 $2.93 $3.21 $3.37 $3.08 $3.04 $3.24 $3.17 $3.36 $3.25 $3.62 $3.88 $3.02 $3.68 $3.29 $2.81 $3.43 $3.44 Confidence Interval Calculator Confidence Interval for a Population Mean, Sigma Known If the population standard deviation is known, we can directly calculate the standard deviation of the sampling distribution (the standard error of the estimate) and use the standardized normal distribution to get a z-multiple, using the Excel function NORMSINV. The margin of error is the z-multiple times the standard error, and it is how far the confidence interval extends on each side of the point estimate. Input Variables: Sample mean (x-bar): 100 Population standard deviation (sigma): 15 Sample size (n): 50 Confidence level: 0.9 < Input the appropriate number for your situation. < Input the appropriate number for your situation. < Input the appropriate number for your situation. < Input the appropriate number for your situation. Intermediate Calculations: Standard error of the estimate: 2.1213203 Prob. in one-tail for this conf level: 0.05 Prob. to use in NORMSINV: 0.95 Z-multiple: 1.645 Confidence Interval: Lower limit: 96.51 Upper limit: 103.49 Margin of error: 3.49 We can be 90% confident that the population mean lies between 96.51 and 103.49 r for your situation. r for your situation. r for your situation. r for your situation. ent that the population mean d 103.49 Confidence Interval Calculator Confidence Interval for a Population Mean, Sigma Unknown If the population standard deviation is not known, we must use the sample standard deviation as an estimate and use it to calculate the standard deviation of the sampling distribution (the standard error of the estimate). We also use the t distribution to get a multiple corresponding to the desired confidence level, using the Excel function TINV. The margin of error is the t multiple times the standard error, and it is how far the confidence interval extends on each side of the point estimate. Input Variables: Sample mean (x-bar): 1000 Sample standard deviation (s): 500 Sample size (n): 70 Confidence level: 0.95 <-- Input the appropriate number for your situation. <-- Input the appropriate number for your situation. <-- Input the appropriate number for your situation. <-- Input the appropriate number for your situation. Intermediate Calculations: Degrees of freedom: 69 Standard error of the estimate: 59.76 Prob. in the tails for this conf level: 0.05 T-multiple: 1.995 Confidence Interval: Lower limit: 880.78 Upper limit: 1119.22 Margin of error: 119.22 We can be 95% confident that the population mean lies between 880.78 and 1119.22 population mean Confidence Interval Calculator Confidence Interval for a Population Proportion From a sample proportion we can calculate the standard deviation of the sampling distribution (the standard error of the estimate), and use the standardized normal distribution to get a z-multiple, using the Excel function NORMSINV. The margin of error is the z-multiple times the standard error, and it is how far the confidence interval extends on each side of the point estimate. Input Variables: Sample proportion (p-bar): 0.43 Sample size (n): 100 Confidence level: 0.95 <-- Input the appropriate number for your situation. <-- Input the appropriate number for your situation. <-- Input the appropriate number for your situation. Intermediate Calculations: Standard error of the estimate: 0.0495 Prob. in one-tail for this conf level: 0.025 Prob. to use in NORMSINV: 0.975 Z-multiple: 1.960 Confidence Interval: Lower limit: 0.3330 Upper limit: 0.5270 Margin of error: 0.0970 We can be 95% confident that the population proportion lies between 0.333 and 0.527 for your situation. for your situation. for your situation. ent that the population proportion Sample Size Estimator Population Mean The inputs to determine the required sample size when taking a sample to estimate a population mean include a planning estimate for the population standard deviation (sigma), the required margin of error (expressed in whatever units sigma is expressed in), and the required confidence level. Inputs: Planning value for sigma: 100 Desired margin of error: 25 Confidence level: 0.95 <-- Input the appropriate number for your situation. <-- Input the appropriate number for your situation. <-- Input the appropriate number for your situation. Intermediate Calculations: Z-multiple: 1.9600 Sigma squared: 10000 M.E. squared: 625 Z-multiple squared: 3.8414588 Results: Sample size needed: 62 End of worksheet (Rounded up to a whole number.) Sample Size Estimator Population Proportion The inputs to determine the required sample size when taking a sample to estimate a population proportion include a planning value for the population proportion (p-star), the required margin of error (expressed in whatever units sigma is expressed in), and the required confidence level. Inputs: Planning value for p-star: 0.5 Desired margin of error: 0.03 Confidence level: 0.95 < Input the appropriate number for your situation. < Input the appropriate number for your situation. < Input the appropriate number for your situation. Intermediate Calculations: Z-multiple: 1.9600 Sigma: 0.25 M.E. squared: 0.0009 Z-multiple squared: 3.8414588 Results: Sample size needed: 1068 End of worksheet (Rounded up to a whole number.)