This week addresses many topics, from continuously distributed variables to statistical sampling plans and confidence interval construction. The questions that follow test your understanding of the statistical concepts introduced this week.
Select any one of the following starter bullet point sections. Review the important themes within the sub questions of each bullet point. The sub questions are designed to get you thinking about some of the important issues. Your response should provide a succinct synthesis of the key themes in a way that articulates a clear point, position, or conclusion supported by research.. If all of the bullet points have been addressed, then you may begin to re-use the bullet points with the expectation that varied responses continue.
You are designing a direct marketing campaign for an online clothing retailer. As part of your design, you quantify the expected response rates by ethnic group. Your definition of the term “ethnicity” follows that of the U.S. Census Bureau (e.g., Hispanic, Asian, African American, etc.). You want to test your campaign using 1,000 randomly selected households, but you want your sample to mimic the US population in terms of the proportion of different ethnicities (e.g., if Hispanics constitute about 12 percent of the US population, 12 percent of your sample should be Hispanic).
- Assess the appropriateness of using a simple random sample as the test’s sampling plan.
- Evaluate other potential sampling plans, and describe why such other sampling plans might be more or less appropriate than using a simple random sample. Support your discussion with relevant examples, research, and rationale.
You are a manager working for an insurance company. Your job entails processing individual claims filed by policyholders. In general, few claims are expensive. Each quarter, you compile a report summarizing key claim statistics, such as the number of claims submitted, the average cost per claim, and the total cost of submitted claims. In the last quarter’s report, you notice a large difference between the mean and the median claim cost, the mean cost being much higher than the median cost.
- Draw a conclusion as to why you might be observing this difference in the data.
- Evaluate whether this information might be useful for determining if the claims data is normally distributed.
- If you conclude that the data is likely normally distributed, explain why. If not, suggest another distribution that might best describe the data. Explain why this distribution would be a more accurate representation of the data.
- Given the large difference between the two measures of central tendency, which of the two measures would you rely on in describing the average claim cost and why? Support your discussion with relevant examples, research, and rationale.
You are an inventory manager working for a large online retailer. As with any retailer, inventory control is one of the critical success factors for the organization. Having too little inventory risks the loss of sales when your company is unable to fulfill an order. However, too much inventory imposes unnecessary costs on the organization. Often, one of the most important pieces of information that can be used to determine how much inventory to have on hand is the rate at which demand occurs for the product.
- Determine what information you would need to construct a confidence interval for the demand that will occur during a month.
- Analyze how the numbers of such a confidence interval might influence the level of inventory that the organization chooses to carry. Support your discussion with relevant examples, research, and rationale.
The final paragraph (three or four sentences) of your initial post should summarize the one or two key points that you are making in your initial response.
- Your posting should be the equivalent of 1 to 2 single-spaced pages (500–1000 words) in length.