MATH221 Statistics for Decision Making Week 6 Lab Name:_______________________ Statistical Concepts: Confidence IntervalsData SimulationNormal Probabilities Short Answer Writing Assignment All answers should be complete sentences. In the Week 2 Lab, you found the mean and the standard deviation for the SLEEP variable for both males and females.Use those values for follow these directions to calculate the numbers again. (From Week 2 Lab: Calculate descriptive statistics for the variable Sleep by Gender.Sort the data by gender by clicking on Data and then Sort.Copy the Sleep of the males from the data file into the Descriptive Statistics worksheet of the Week 1 Excel file.[Write down the mean and standard deviation.] These are sample data. Then, copy and paste the female data into the Descriptive Statistics workbook and do the same.Keep three decimal places.) You will also need the number of males and the number of females in the dataset.You can actually count these in the dataset. Then use the Week 5 spreadsheet to calculate the following confidence intervals.The male confidence interval would be one calculation in the spreadsheet and the females would be a second calculation. Give and interpret the 95% confidence intervals for males and a second 95% confidence interval for females on the SLEEP variable.Which is wider and why? Give and interpret the 99% confidence intervals for males and a second 99% confidence interval for females on the SLEEP variable.Which is wider and why?Give and interpret the 95% confidence interval for the size of students’ shoes. Give and interpret the 99% confidence interval for the size of students’ shoes.Compare the 95% and 99% confidence intervals for the size of students’ shoes. Explain the difference between these intervals and why this difference occurs. Find the mean and standard deviation of the DRIVE variable by copying that variable into the Week 1 spreadsheet. Use the Week 4 spreadsheet to determine the percentage of data points from that data set that we would expect to be less than 25.To find the actual percentage in the dataset, sort the DRIVE variable and count how many of the data points are less than 25 out of the total 35 data points.That is the actual percentage.How does this compare with your prediction?What percentage of data would you predict would be between 25 and 50 and what percentage would you predict would be more than 50 miles?Use the Week 4 spreadsheet again to find the percentage of the data set we expect to have values between 25 and 50 as well as for more than 50.Now determine the percentage of data points in the dataset that fall within each of these ranges, using same strategy as above for counting data points in the data set.How do each of these compare with your prediction and why is there a difference? We need to find the confidence interval for the SHOE SIZE variable.To do this, we need to find the mean and standard deviation with the Week 1 spreadsheet.Then we can the Week 5 spreadsheet to find the confidence interval.This does not need to be separated by males and females, rather one interval for the entire data set. First, find the mean and standard deviation by copying the SHOE SIZE variable and pasting it into the Week 1 spreadsheet.Write down the mean and the sample standard deviation as well as the count. Open the Week 5 spreadsheet and type in the values needed in the green cells at the top to find the confidence interval. Change the confidence level to 99% to find the 99% confidence interval for the SHOE SIZE variable. Mean: ______________Standard deviation: ____________________ Predicted percentage: Actual percentage: Comparison ___________________________________________________ ______________________________________________________________ Predicted percentage between 25 and 50: ______________________________ Actual percentage: Predicted percentage more than 50 miles: Actual percentage: ___________________________________________ Comparison ____________________________________________________ _______________________________________________________________ Why?__________________________________________________________ ________________________________________________________________

PART1: Assessing NormalityIn this module, you explore the normal distribution. A standard normal distribution has a mean of zero and a standard deviation of one. The z-score statistic converts a non-standard normal distribution into a standard normal distribution allowing us to use Table A-2 in your textbook (or whatever technology you want!) and report associated probabilities.This discussion combines means, sample standard deviation, z-score, and probability. You are encouraged to complete the textbook reading, review the narrated Ppts., and start the MyStatLab Homework before starting this discussion.ScenarioThe following table reports simulated annual flying squadron costs (in millions of dollars) at the following locations:Module 4 Airshow Template.xlsxCompleteUse Microsoft Excel and StatDisk to complete the Flying Squadron Costs table for the aircraft type listed below:If your last name begins with the letter A through L, compute the mean costs (x-bar) and sample standard deviation (s) using the B-52 data; use the Kadena mean cost (x) in your z-score and probability calculations.If your last name begins with the letter M through Z, compute the mean costs (x-bar) and sample standard deviation (s) using the F-35 data; use the Charleston mean cost (x) in your z-score and probability calculations.Report your values to two decimal places (i.e., 0.12) except for probability (four decimal places). Report probability, i.e., area, (to the right of your z-score) values to four decimal places (i.e. p = 0.1234).Your StatDisk results should look very similar to this image:Save your work as separate files to your computer and then read the Canvas instructions on How do I embed an image in a discussion reply as a student? (Links to an external site.)Links to an external site.Post & DiscussEmbed the images of your spreadsheet and StatDisk results in the discussion area along with a narrative (interpretation and understanding) of your findings and the responses to the questions below.Do these costs appear to come from a population that has a normal distribution? Why or why not?Can the mean of your data sample be treated as a value from a population having a normal distribution? Why or why not?Did an “unusually low” or “unusually high” z-score value occur? See Ppts.Was the associated z-score probability value less than 0.05 (p < 0.05); meaning a “significantly low” or “significantly high” event? If yes, what are the implications for the base and/or aircraft?What were your findings? Hint: focus on the calculated mean, standard deviation, and z-score (include probability) to interpret your results.You should make your initial post before the fourth day of the module week (Friday) to receive full credit. Return at least twice later in the module week to provide meaningful (substantive) comments to two or more of your classmates' posts. DO NOT “post and run” – making all three posts in the same visit. You need multiple visits to the discussion area to gain multiple perspectives by reading all of the posts and replies.Review the Discussion Rubric for detailed grading information.PART2Flying Squadron Costs ReportAssignmentReport the CostsNow that you have calculated simulated annual flying squadron costs, you are required to report your findings. Remember the focus for this module is the normal distribution; specifically mean, standard deviation, z-score, and probability; what these descriptive and inferential statistics physically mean and how they are used in a simulated “real-world” problem.You are encouraged to calculate all row and column values for mean, standard deviation, z-score, and probability so that the entire “data picture” is available. (Hint: Are there any unusual events? Either by aircraft or base?)Report the costs in a Memorandum of Understanding (MOU). Your MOU should be a maximum of one page with one-inch margins using 11 point font and consist of only the following three paragraphs:Introduction - Prepare the audience for what they are about to read.Results - The facts.Conclusion(s) - Results are fact-based, concise and to the point; actionable.Review the Writing Suggestions page for tips. Use this format for your document.MEMORANDUM OF UNDERSTANDINGTO: 97th AMW - USAFFROM: Your NameDATE: Add Assignment Due DateSUBJECT: Determined by StudentSubmitSave your assignment using a naming convention that includes your first and last name and the activity number or description (i.e., STAT_211_Last_Name_First_Name_Module_4). Do not add punctuation or special characters.This assignment will automatically be checked through Turnitin, a service that checks your work for improper citation or potential plagiarism by comparing it against a database of web pages, student papers, and articles from academic books and publications.Review the Assignment Rubric for detailed grading information.