Description Week 12 – Signature Assignment: Perform One-Way Analysis of Variance Tests Instructions For this task, write a paper using the following structure: Begin with a one or two-paragraph introduction that summarizes the meaning of the reading material. Answer all of the questions included in Parts 1 and 2 below. Be sure to answer questions using complete sentences and show all work in your calculations. Provide a written conclusion, when appropriate, for the problem that you are addressing. Include a paragraph or two that explains the information that you learned in the assignment. Be sure to include a course reflection since this is the final assignment. Problems in Part 2 should be completed using methods outlined in the textbook or performing a one-way ANOVA with SPSS or Excel; refer to the website under your weekly resources. Part 1 What are the required conditions for a one-way ANOVA? Give an explanation of the F statistic. Explain the shape of the F distribution. Suppose that there are three different populations we want to compare, say P1, P2 and P3. Each of these populations are normal. A random sample from each population is taken and the results are given below. P1 P2 P3 10 6 5 12 8 9 9 3 12 15 0 8 13 2 4 a) Find the sample means and sample variance for each sample. Use Excel and record the results in your Word document. b) Combine all samples and find the mean of the data set with 15 data points. Call this the grand mean. c) Create a graph that illustrates the sample means and the grand mean. Copy and paste your graph into your Word document. d) Based on parts a, b and c do the sample means appear to be approximately equal? 4. Using the data from Problem 3, use the formulas given in the textbook to calculate F using the MSG and MSE. Part 2 Using the data from Problem 3 in Part 1, perform a one-way ANOVA test. Be sure to give the hypotheses, the value of F, the p-value, and the conclusion. Copy and paste the software output into your Word document. A food processing plant typically contain fungus spores. If the ventilation system is not adequate, this can have a serious effect of the health of employees. To determine the amount of spores present, random air samples are pumped to a certain plate, and the number of “colony-forming units (CFUs)” are determined after time allowed for incubation. The data from the room of a plant that slaughters 35,000 turkeys per day, which are obtained during the four seasons of the year, is given below. The units are in CFUs per cubic meter. Fall Winter Spring Summer 1231 384 2105 3175 1254 104 701 2526 1088 97 842 1090 1124 401 1243 1987 a) Examine the data using exploratory data analysis tools. Create at least one graph comparing means. b) Perform an one-way ANOVA to determine is the effect of the season is statistically significant. Use the four-step method discussed in the textbook. Be sure to give a practical conclusion. Assume the populations are normally distributed and the variances are roughly equal. Copy and paste the results of the test into your Word document. An appliance manufacturing company want to test microwave ovens being sold. The researcher has identified three different types based on the number of watts of the ovens. Three random samples are taken and the data is given below. Watts 800 900 1000 180 235 225 175 135 225 200 160 190 170 230 215 190 250 250 180 200 230 185 200 170 160 210 179 195 199 200 a) Create a table of group sample means and sample standard deviations. b) Create an appropriate graph. Copy and paste the graph into your Word document. Do the means appear to be equal based on your graph? c) Carry out the ANOVA. Report the F statistic, its p-value and state your conclusion. Copy and paste the results of the ANOVA test into your Word document. Part 3 Provide a detailed course reflection regarding how the knowledge gained in this course provided you with an understanding of the role of statistics in business applications. Be sure to offer a detailed and succinct explanation of the information that you have gained from the course. The personal insights paper serves as the foundation for your discussion with your course instructor and possibly other students. Support your insights paper with a minimum of three (3) external resources. In addition to these specified resources, other appropriate scholarly resources, including older articles, may be included. Your Course Reflection must include, but is not limited, to the following: a) An Introduction, examples of business statistics and data analysis that may be useful in your discipline. b) The most difficult and least difficult statistical tests. Explain why. c) Which tools within this course were the most helpful? Has the course supported a decision to utilize a quantitative methodology for your prospective dissertation topic? Explain. d) Final conclusions about the course. Length: approx. 10 pages References: Include a minimum of three scholarly peer-reviewed resources.
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