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GRINNELL MAT 209 - SAMPLE Final Exam ANOVA

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Sample Final Exam ANOVAIron-deficiency anemia is the most common form of malnutrition in developing countries, affecting about 50% of children and women and 25% of men. Iron pots for cooking foods had traditionally been used in many of these countries, but they have been largely replaced by aluminum pots, which are cheaper and lighter: Some research has suggested that food cooked in iron pots will contain more iron than food cooked in aluminum or clay pots. The following study was designed to investigate the issue of iron content of some Ethiopian foods cooked in aluminum, clay, and iron pots. The iron in the food is measured in milligrams of iron per 100 grams of cooked food. Here is the data: Meat Legumes Vegetables Aluminum 1.77 2.36 1.96 2.14 2.4 2.17 2.41 2.34 1.03 1.53 1.07 1.3 Clay 2.27 1.28 2.48 2.68 2.41 2.43 2.57 2.48 1.55 0.49 1.68 1.82 Iron 5.27 5.17 4.06 4.22 3.69 3.43 3.84 3.72 2.45 2.99 2.8 2.92The following summary data was collected for the above data:Pot N Mean Median StDevAluminum 12 1.873 2.050 0.522Clay 12 2.012 2.340 0.661Iron 12 3.713 3.705 0.884Fill in the following1-way ANOVA table to test if there is a difference in the mean iron content of each pot.Source df SS MS F p_____________________________________________________________ TotalComplete the following 2-way ANOVA which also used the above data:Source DF SS MS F PPot 2 25.202 Food 2 9.730 Interaction 4 2.568 Error ________________________________________Total 35 41.612Draw a main effects and interaction plot using the above data.Use multiple comparisons to test the difference between pots.Use contrasts to test if the µmeat = ½(µLegumes + µvegetables) and µLegumes = µvegetablesUse contrasts to test if the µiron = ½(µclay + µAlum) and µclay = µAlumSample Final Exam ANOVAHow are smoking habits of student related to their parents' smoking? Here is a two-way table from a survey of student in eight Arizona high schools:Student smokes Student does not smokeBoth parents smoke 400 1380One parent smokes 416 1823Neither parent smokes 188 1168Step 1) What is your null and alternative hypothesis?Step 2) What is the value of your test statistic?Step 3) Compare the test statistic to the appropriate table value.Step 4) Do you fail to reject or reject Ho? How are smoking habits of student related to their parents' smoking?1) North Caroline State University studied student performance where one question of interest is the relationship between time spent in extracurricular activities and whether a student earned a C or better in a course. Here are data for 119 students who answered a question about extracurricular activities:Extracurricular activities (hours per week)Less than 2 hours 2-12 hours More than 12 hoursC or Better 11 68 3D or F 9 23 5Step 1) What is your null and alternative hypothesis?Step 2) What is the value of your test statistic?Step 3) Compare the test statistic to the appropriate table value.Step 4) Do you fail to reject or reject Ho? Do the number of hours spent in extracurricular activities affect grades?2) A manufacturing plant tested 3 new machines to identify which machine produced the best quality product. Below are the data for the 3 machines (higher quality numbers are better). Use a 1 way ANOVA table to determine if there is a significant difference between machines.Machine 1: 75 80 85 90Machine 2: 80 85 80 80Machine 3: 65 70 65 75ANOVASource df SS MS F p-valueGroupsErrorTotal What is your null and alternative hypothesis?What is the numerator and denominator degrees of freedom for the F value? Do you fail to reject or reject Ho? Is there a difference between machines? Which would you suggest.Draw a scatterplot of the data.The finance department just notified you that machine 1 will cost $250,000, machine 2 will cost $140,000, and Machine 3 will cost $135,000. The company president asks you to suggest a machine topurchase, what would you suggest? Why?Sample Final Exam ANOVA4) A manufacturing plant tested 2 new machines to identify which machine produced the best quality product. Below are the data for the 2 machines (higher quality numbers are better). In addition to testing machines, the company also chose to test 2 types of material that can be used on either machine. Use the following 2 way ANOVA table to determine if there is a significant difference between machines.Analysis of Variance for quality_Source DF SS MS F PMachine 1 3.13 3.13 0.33 0.595material 1 28.13 28.13 3.00 0.158Interaction 1 78.13 78.13 8.33 0.045Error 4 37.50 9.38Total 7 146.88Material A Material BMachine 1 75 80 85 90Machine 2 85 80 80 80Draw a main effect plots of the data. Draw an interaction plot of the data Machine 1 Machine 2 Material A Material BThe president of the company announces that you would definitely use material B. Your coworker saidthat since the p-value for machine is so large, it makes no difference if you choose to use machine 1 or 2. Is he right? Why or why not?5) What 3 assumptions are we making when using an ANOVA table. Explain how this could impact the results of your test.6) Xi ~ N(x, 9) Yj ~N(y, 25) nx = 20 ny = 35 Test H1: x  y at  = .1You manage a medical supply company and 2 different suppliers want you to purchase their medical syringes. Before you select a supplier you want to test the average strength of each syringe ( in 3_a). The higher the average strength the better. What would you do? Discuss confidence/significance in your answer.75777981838587891 2 3 4798081828384851 2 3 45.2527  YXYandXSample Final Exam ANOVA7) A manufacturing engineer wants to study the amount of time required to assemble a piece of equipment. She is particularly interested in how the assembly time varies among workers. To study this question she selects 4 workers at random and records the assembly times for 6 jobs for each worker.Worker 1 Worker 2 Worker 3 Worker 420 16 18 2122 23 20 1721 20


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