Mathematics

This assignment is intended to help you learn how to apply statistical methods when analyzing operational data, evaluating the performance of current marketing strategies, and recommending actionable business decisions. This is an opportunity to build critical-thinking and problem-solving skills within the context of data analysis and interpretation. You’ll gain a first-hand understanding of how data analytics supports decision-making and adds value to an organization.Scenario:Pastas R Us, Inc. is a fast-casual restaurant chain specializing in noodle-based dishes, soups, and salads. Since its inception, the business development team has favored opening new restaurants in areas (within a 3-mile radius) that satisfy the following demographic conditions:Median age between 25 – 45 years oldHousehold median income above national averageAt least 15% college educated adult populationLast year, the marketing department rolled out a Loyalty Card strategy to increase sales. Under this program, customers present their Loyalty Card when paying for their orders and receive some free food after making 10 purchases.The company has collected data from its 74 restaurants to track important variables such as average sales per customer, year-on-year sales growth, sales per sq. ft., Loyalty Card usage as a percentage of sales, and others. A key metric of financial performance in the restaurant industry is annual sales per sq. ft. For example, if a 1200 sq. ft. restaurant recorded $2 million in sales last year, then it sold $1,667 per sq. ft.Executive management wants to know whether the current expansion criteria can be improved. They want to evaluate the effectiveness of the Loyalty Card marketing strategy and identify feasible, actionable opportunities for improvement. As a member of the analytics department, you’ve been assigned the responsibility of conducting a thorough statistical analysis of the company’s available database to answer executive management’s questions.Report:Write a 750-word statistical report that includes the following sections:Section 1: Scope and descriptive statisticsSection 2: AnalysisSection 3: Recommendations and ImplementationSection 1 – Scope and descriptive statisticsState the report’s objective.Discuss the nature of the current database. What variables were analyzed?Summarize your descriptive statistics findings from Excel. Use a table and insert appropriate graphs.Section 2 – AnalysisUsing Excel, create scatter plots and display the regression equations for the following pairs of variables:In your report, include the scatter plots. For each scatter plot, designate the type of relationship observed (increasing/positive, decreasing/negative, or no relationship) and determine what you can conclude from these relationships.Section 3: Recommendations and implementationBased on your findings above, assess which expansion criteria seem to be more effective.Could any expansion criterion be changed or eliminated? If so, which one and why?Based on your findings above, does it appear as if the Loyalty Card is positively correlated with sales growth? Would you recommend changing this marketing strategy?Based on your previous findings, recommend marketing positioning that targets a specific demographic. (Hint: Are younger people patronizing the restaurants more than older people?)Indicate what information should be collected to track and evaluate the effectiveness of your recommendations. How can this data be collected? (Hint: Would you use survey/samples or census?)

1.) Consider the two-round bargaining game. The minimum the seller will sell his home for 188,000 and the maximum the buyer is willing to pay is $200,000. Both players know these two amounts and are bargaining over the difference (M=$12,00). Assume the disagreement values are zero for both players. Player 1 moves first by making a proposal and Player 2 can accept and reject. If player 2 rejects Player’s 1 proposal, then Player 2 gets to make a proposal, which Player 1 can reject and accept. The game is then over. Suppose the both players discount the future income at the rate d=0.2 per period. That is, $0.20 now is equivalent to $1,00 received next round. Find the equilibrium for this 2-round game. What is the sale price of the home? Which player gets the larger share of M?2.) In Depositor versus Saving & Loan Association (S&L), suppose that the S&L can invest $100,000 in a junk bond (the official name for this sort of security is high-yield bond) with the following rates of return: with high effort (H represents high research effort), the probability is 0,98 that the rate of return is 15% and 0.02 that the money vanishes; with low effort (L represents low research effort), the probability is 0.92 that the rate of return is 15% and 0.08 that the money vanishes. The rate of return on government bonds is 4%. After paying off the depositor, the S&L is left with $2000 minus research cost. Draw the extensive form and solve. Where should the depositor put the money?3.) Find time path (general solution) of P and U, given_P= (1/4) – 2U + n dP/dt = 1/2(P-n) dU/dt = – (m-p)4.) Consider a model of a competitive market in which price is adjust to excess demand or supply and firms enter or exit the industry if profits or losses are being made. Price adjusts to excess demand according to ?=(qD-qS), >0 where = a+bp is the demand function, =mN is the supply function, p is price, N is the number of firms in the industry, is speed-of adjustment coefficient. Making these substitutions gives ?=(a+bp-mN). The number of firms adjusts according to ?=z (p – ?), z>0 where ? is the fixed average cost of production. Firms enter (?>0) if price exceeds average cost (positive profits) and exit if price is less than the average cost (negative profit). Solve this system of differential equations for price and number of firms.5.) Suppose you have won $200,000 in the state lottery and you have decided to retire on your winnings. Suppose you deposit your winnings in a bank that pays 8% annual interest (compounded annually) and make yearly withdrawals of $30,000. (Hint: if periodic withdrawals, each of amount d, are deposited in a bank account whose initial amount is that pays interest at a rate r per period, then the difference equation that describes the total amount in the account after n periods is = (1+r) – d)a. What are the difference equation and initial condition that describes the future value of your account?b. Will you ever run out of money? If so, when?6.) Consider the following model, = s , = k ( – ), = where s is the marginal propensity to save and k is the acceleration coefficient. The third equation states the equilibrium condition for the determination of national income (ex ante saving = ex ante investment). Derive the general solution for . Comment on your result. (Let = for t=0)

If I have two Products (Product A and Product B) and I want to ship these products to customers as follows:Product A (# of units: 4000)Product B (# of units: 4000)The products must be shipped through using Pallets.Each Pallet can hold 1000 units of Products A or 2000 units of Product B.Transportation cost for both Products (A and B) is the same. $1 dollar per pallet.Question: How many pallets I need to ship theses products? What is the final price the customer must for shipment?

CHAPTER 5: A SURVEY OF PROBABILITY CONCEPTSVideo #29: How to build a contingency table with Pivot table (Length: 3:40)Video #30: How to use Permut and Combin formulas (3:47)Video #31: How to apply Bayes Theorem (Length: 4:33CHAPTER 6: DISCRETE PROBABILITY DISTRIBUTIONSVideo #32: How to build and graph discrete probability distribution (Length: 3:36)Video #33: How to apply binomial distribution (Length: 4:48)Video #34: How to apply hypergeometric distribution (Length: 4:41)Video #35: How to apply Poisson.dist (Length: 3:31)

case writeup:around 2-page reflection write-up, 400-600 words • 1 paragraph synopsis of what is the data source, methods, and approach • 2-3 paragraph: What did you find more insightful? What was most counterintuitive?ALSO, raise and write 3-5 insightful and critical questions (about the statistics, economic, consumer analysis,… overall about the class title” BIG DATA CONSUMER ANALYTICS) for the case.

**Reference previous order**SPSS StatisticsAssignment ContentAccess the SPSS® Data Sets in the Course Resources > Student Success Guide to download the data set for this assignment.Open dataset SAQ (Item 3 Reversed).sav in SPSS®.his exercise must be completed on the four subscales below, and you should, therefore, produce four reliability analyses. Subscale 1 (Fearof statistics): items 1, 3, 4, 5, 12, 16, 20, 21 Subscale 2 (Peerevaluation): items 2, 9, 19, 22, 23Subscale 3 (Fearof computers): items 6, 7, 10, 13, 14, 15, 18Subscale 4 (Fear of mathematics): items 8, 11, 17 Using the directions outlined in Section 18.10 (Ch. 18) of Field (2018), conduct a reliability analysis.Note: Access to Ch. 18 can be found in the Week 3 Optional Activities.Post the output from your reliability analysis into a Microsoft® Word document. Also, include responses to the following questions:What did the results tell you about the reliability of the scale?What actions can be taken by a researcher to improve the reliability of a scale?

State whether each equation is true or false for the values of the variables given

Reflect & Write Previous knowledge/skill and attitude (sometimes referred to as “mindset”) are important foundations for learning. In this first discussion, reflect on these two foundations and write a two-paragraph response (at least 500 words in total) for each of the following two areas to begin your practice of communicating technical information. Past Think back to when you were in your early school days and reflect on your mathematical experiences. Be sure to concentrate on you, rather than on the influences of teachers, parents, siblings, etc. Some questions to prod your thinking include: What study habits or classroom activities helped you learn math? Which ones were not helpful? Did group activities help you learn math, help improve your grade, or both? Did you have different study habits for your math classes than for your other classes? If so, why? Present Think about your college experiences with math. If this is your first college mathematics class, answer these questions with how you think this semester will go. Have your study habits changed or remained the same? Are they working? Are there any modifications that you have made, or plan to make, now that you are in an online math class?  In either section, Past or Present, refer to at least two of the Learning Outcomes listed in the syllabus to connect your memories to this class. Review the course syllabus located in the navigation menu. Post & Reply Post your 500-word, two-paragraph response by the end of the fourth day of the module week. Then, read your classmates’ posts and reply to at least two with observations that add to a conversation about the course topics. You must make your initial post before you can see the posts of your classmates. Please read these instructions for information on accessing the discussion rubric.  (Links to an external site.)

No length requirements Suppose that you have two sets of data to work with. The first set is a list of all the injuries that were seen in a clinic in a month’s time. The second set contains data on the number of minutes that each patient spent in the waiting room of a doctor’s office. You can make assumptions about other information or variables that are included in each data set. For each data set, propose your idea of how best to represent the key information. To organize your data would you choose to use a frequency table, a cumulative frequency table, or a relative frequency table? Why? What type of graph would you use to display the organized data from each frequency distribution? What would be shown on each of the axes for each graph?

Scenario Background: A marketing company based out of New York City is doing well and is looking to expand internationally. The CEO and VP of Operations decide to enlist the help of a consulting firm that you work for, to help collect data and analyze market trends. You work for Mercer Human Resources. The Mercer Human Resource Consulting website lists prices of certain items in selected cities around the world. They also report an overall cost-of-living index for each city compared to the costs of hundreds of items in New York City (NYC). For example, London at 88.33 is 11.67% less expensive than NYC. More specifically, if you choose to explore the website further you will find a lot of fun and interesting data. You can explore the website more on your own after the course concludes. https://mobilityexchange.mercer.com/Insights/ cost-of-living-rankings#rankings Assignment Guidance: In the Excel document, you will find the 2018 data for 17 cities in the data set Cost of Living. Included are the 2018 cost of living index, cost of a 3-bedroom apartment (per month), price of monthly transportation pass, price of a mid-range bottle of wine, price of a loaf of bread (1 lb.), the price of a gallon of milk and price for a 12 oz. cup of black coffee. All prices are in U.S. dollars. You use this information to run a Multiple Linear Regression to predict Cost of living, along with calculating various descriptive statistics. This is given in the Excel output (that is, the MLR has already been calculated. Your task is to interpret the data). Based on this information, in which city should you open a second office in? You must justify your answer. If you want to recommend 2 or 3 different cities and rank them based on the data and your findings, this is fine as well. Deliverable Requirements: This should be ¾ to 1 page, no more than 1 single-spaced page in length, using 12-point Times New Roman font. You do not need to do any calculations, but you do need to pick a city to open a second location at and justify your answer based upon the provided results of the Multiple Linear Regression. The format of this assignment will be an Executive Summary. Think of this assignment as the first page of a much longer report, known as an Executive Summary, that essentially summarizes your findings briefly and at a high level. This needs to be written up neatly and professionally. This would be something you would present at a board meeting in a corporate environment. If you are unsure of an Executive Summary, this resource can help with an overview. What is an Executive Summary? Things to Consider: To help you make this decision here are some things to consider: Based on the MLR output, what variable(s) is/are significant? From the significant predictors, review the mean, median, min, max, Q1 and Q3 values? It might be a good idea to compare these values to what the New York value is for that variable. Remember New York is the baseline as that is where headquarters are located. Based on the descriptive statistics, for the significant predictors, what city has the best potential? What city or cities fall are below the median? What city or cities are in the upper 3rd quartile?