Progress CheckUse this activity to assess whether you and your peers can: Under appropriate conditions, conduct a hypothesis test about a mean for a matched pairs design. State a conclusion in context.ContextGosset's Seed Plot DataWilliam S. Gosset was employed by the Guinness brewing company of Dublin. Sample sizes available for experimentation in brewing were necessarily small. At that time, Gosset contacted a famous statistician Karl Pearson (1857-1936) and was told that there were no techniques for developing probability models for small data sets. Gosset studied under Pearson, and the outcome of his study was perhaps the most famous paper in statistical literature, "The Probable Error of a Mean" (1908), which introduced the T-distribution.Since Gosset was employed by Guinness, any work he produced would be owned by Guinness, so he published under a pseudonym, "Student"; hence, the T-distribution is often referred to as Student's T-distribution.To illustrate his analysis, Gosset used the results of seeding 11 different plots of land with two different types of seed: regular and kiln-dried. He wanted to determine if drying seeds before planting increased plant yield. Since different plots of soil may be naturally more fertile, this confounding variable was eliminated by using the matched pairs design and planting both types of seed in all 11 plots.The resulting data (corn yield in pounds per acre) are as follows.PlotRegular seedKiln-dried Seed11903200921935191531910201142496246352108218061961192572060212281444148291612154210131614431115111535We use these data to test the hypothesis that kiln-dried seed yields more corn than regular seed.Because of the nature of the experimental design (matched pairs), we are testing the difference in yield.PlotRegular seedKiln-dried SeedDifference119032009–10621935191520319102011–10142496246333521082180–7261961192536720602122–62814441482–38916121542701013161443–1271115111535–24Note that the differences were calculated: regular − kiln-dried.VariablesRegular seed: regular seeds that were traditionally used for plantingKiln-dried seed: seeds that were kiln-dried before plantingDataOpen the seeds datafile in the Stats at Cuyamaca College group on StatCrunch (directions - opens in a new tab).PromptState the hypotheses and define the parameter.Checking conditions: Since Gosset invented the T-distribution, we will assume that his sample meets the conditions and proceed with the T-test. Regardless, answer these questions to demonstrate your understanding of the conditions for use of the T-model.But first you will need to review the dotplots for the data (opens in a new tab). Which graph is used to check conditions? Why?What do we look for in the graph to verify that conditions are met?What else do we need to know about the sample of seeds before using the T-test?Use StatCrunch to find the T-score and the P-value. Hint: as you work through the StatCrunch directions, keep in mind that we want to calculate the differences as regular − kiln-dried . So you will choose Regular seed for Sample 1 and Kiln-dried seed for Sample 2. (directions)Copy the information in the StatCrunch output window and paste it into the textbook with your response.State a conclusion based on the context of this scenario.

Summary and Descriptive Statisticsthere is often the requirement to evaluate descriptive statistics for data within the organization or for health care information. Every year the National Cancer Institute collects and publishes data based on patient demographics. Understanding differences between the groups based upon the collected data often informs health care professionals towards research, treatment options, or patient education.Using the data on the "National Cancer Institute Data" Excel spreadsheet, calculate the descriptive statistics indicated below for each of the Race/Ethnicity groups. Refer to your textbook and the Topic Materials, as needed, for assistance in with creating Excel formulas.Provide the following descriptive statistics:Measures of Central Tendency: Mean, Median, and ModeMeasures of Variation: Variance, Standard Deviation, and Range (a formula is not needed for Range).Once the data is calculated, provide a 150-250 word analysis of the descriptive statistics on the spreadsheet. This should include differences and health outcomes between groups.APA style is not required, but solid academic writing is expected.This assignment uses a rubric. Please review the rubric prior to beginning the assignment to become familiar with the expectations for successful completion.

Traveling Salesman ProblemFor this Critical Thinking assignment, you will solve a real-world optimization problem using graph theory.Part I: Complete the following steps: Select a real-world optimization problem that is an example of the Traveling Salesman Problem (TSP). Create a graph modeling the real-world scenario corresponding to the problem. Use weights to represent the variable that you are optimizing. Find an optimal solution for the problem using the concepts studied in this module. Part II: Based on your work in Part I, discuss the following: Discuss your rationale for your choice of the real-world optimization problem. How were you able to identify that it was an example of the TSP? Why is this example relevant? Describe how you created the graph modeling the real-world scenario corresponding to the problem. Determine if the graph is complete. If so, use your graph to describe the formula for computing the number of Hamilton circuits. Explain in detail how you solved the problem. Describe a method for finding a non-optimal solution to the problem. Consider another variable that could be optimized in the problem. How would your answers to Part I be affected by this change? Discuss the advantages of using graph theory to solve this problem. Requirements:You must submit TWO files for this assignment. The first file should contain the computations, graphs, diagrams, etc., associated with the questions in Part I. This file may be formatted as a numbered list of answers. Unless stated in the problem, a narrative discussion is not required, but you must provide enough information to show how you arrived at the answer.The second file should be a 2-3-page narrative paper, written in APA format, associated with the situation described in Part II. Specific requirements for the paper are provided below: