You are a marketing manager for a company that makes ready-to-eat breakfast cereals. Your company recently initiated a loyalty program for consumers, which resulted in a large purchaser database. The brand managers are eager to mine the available data, which they can use to design more effective promotional programs. The management of your organization believes that to be effective, these programs have to take into account significant cross-region (i.e., the East Coast, the West Coast, the Midwest, and the South) purchase differences. Your task is to test the hypothesis that there are significant cross-region differences in purchasing patterns. Management has suggested that you use six different two-way comparisons (directly comparing each region with every other region), with each two-way comparison being suggested at the 5% level.Assess how appropriate management’s proposed use of hypothesis testing would be to validate management’s belief in cross-region purchase differences.Explain the goal of this hypothesis testing experiment.Describe the mechanics of this hypothesis testing process.Explain why the organization would go through the trouble of hypothesis testing in this situation. Support your discussion with relevant examples, research, and rationale.

Option 2 Scenario Option 2 Data SetThis week you will begin working on Phase 2 of your course project. Using the same data set and variables for your selected topic, add the following information to your analysis:Discuss the importance of constructing confidence intervals for the population mean. What are confidence intervals?What is a point estimate?What is the best point estimate for the population mean? Explain.Why do we need confidence intervals? Find the best point estimate of the population mean.Construct two confidence intervals for the population mean: a 95% confidence interval and a 99% confidence interval. Assume that your data is normally distributed and the population standard deviation is unknown. Please show your work for the construction of these confidence intervals and be sure to format your equations to fit the appropriate form (may need editing here). Write a paragraph that correctly interprets the confidence intervals in context of your selected topic. Compare and contrast your findings for the 95% and 99% confidence intervals. Did you notice any changes in your interval estimate? Explain.What conclusion(s) can be drawn about your interval estimates when the confidence level is increased? Explain.

R is a free statistical software that is frequently and widely used. Go to R-Project for Statistical Computing (Links to an external site.)Links to an external site. to download the R software to your computer (follow the instructions provided in the attached R Installation Instructions sheet). The R Project website (Links to an external site.)Links to an external site. provides a brief introduction to R that you may also want to review. Like SAS, R is code-driven software that provides computation and graphics easily. This means that you need to write code in order to obtain the results. In this CT assignment, you will write code to find the probabilities. Some R example code to find the probabilities under specific distributions are given in Section 1.11 of zyBooks. For each problem, write an R code to compute each probability.(a) Binomial Distribution: X ~ Bin(10, 0.7) (i) P(X = 2) (ii) P(X < 2) (iii) P(X > 2) (iv) P(1 < X < 7)(b) Normal Distribution: X ~ N(0, 4). Note that variance is 4 and, hence, the standard deviation is 2. (i) P(X < 3) (ii) P(X > 3) (iii) P(1 < X < 3)(c) Choose either (a) or (b) and interpret the results in a real-life scenario. Make sure to define X and interpret each probability. For parts (a) and (b), take screenshots of R codes and the answers. Copy and paste the screenshot(s) into a Word document and submit the Word file in Canvas.