Statistics – One-Way Analysis of Variance Tests

Part 1

1. What are the required conditions for a one-way ANOVA?
2. Give an explanation of the F statistic. Explain the shape of the F distribution.
3. 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

1. 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) Use Excel to 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?
2. Using the data from Problem 3, use the formulas given in the textbook to calculate F using the MSG and MSE.

Part 2

1. 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.
2. 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

1. 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.

1. 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

1. 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?

1. 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 (4 paragraphs, 5 sentences each)

Provide a detailed write up regarding how the knowledge gained (statistics) providesone with an understanding of the role of statistics in business applications.

Write four paragraphs (5 sentences each); on how statistics may, assist with research (statistical analysis) on legacy computers in the military spread over 3 continents.

Your Reflection must include, but is not limited, to the following:

1. a) An Introduction, examples of business statistics and data analysis that may be useful in gathering and analyzing legacy computers spread over 3 continents.
   b) The most difficult and least difficult statistical tests. Explain why.
   c) Which tools (in statistics)would be most helpful?