ANOVA and Confidence Intervals: Comparing Yields of Corn Plants and Fish Development, Exams of Data Analysis & Statistical Methods

Download ANOVA and Confidence Intervals: Comparing Yields of Corn Plants and Fish Development and more Exams Data Analysis & Statistical Methods in PDF only on Docsity! Stat/For/Hort 571 Clayton and Gangnon November 20, 2001 Midterm II Name: For the section that you attend please indicate: Instructor:(circle one) Clayton Gangnon TA: (circle one) Cheng Li Song Instructions: 1. This exam is open book. You may use textbooks, notebooks, class notes, and a calculator. 2. Do all your work in the spaces provided. If you need additional space, use the back of the preceding page, indicating clearly that you have done so. 3. To get full credit, you must show your work. Partial credit will be awarded. 4. Some partial computations have been provided on some questions. You may find some but not neces- sarily all of these computations useful. You may assume that these computations are correct. 5. Do not dwell too long on any one question. Answer as many questions as you can. 6. Note that some questions have multiple parts. For some questions, these parts are independent, and so you can work on part (b) or (c) separately from part (a). For graders’ use: Question Possible Points Score 1 28 2 20 3 20 4 16 5 16 Total 100 1. (a) An experiment was conducted to study how different insecticides might influence the yield of corn plants which have been sprayed with the insecticides. For each insecticide there were several plots used; the assignment of the insecticides to the plots was done completely randomly. The following table summarizes the information available from this experiment. Insecticide 1 x̄1· = 18.3 s21 = 1.84 n1 = 8 Insecticide 2 x̄2· = 20.1 s22 = 1.94 n2 = 6 Insecticide 3 x̄3· = 20.2 s23 = 0.51 n3 = 5 Insecticide 4 x̄4· = 19.6 s24 = 0.38 n4 = 8 Complete the following ANOVA Table and perform a test of the null hypothesis that the popu- lation mean yields corresponding to the four insecticides are all equal, versus the alternative that they are not all equal. 1 Stat/For/Hort 571 Clayton and Gangnon November 20, 2001 Source df SS MS Insecticide Error Total 43.47 (b) (You can answer this question independently of part (a).) PCBs are chemical compounds that are used in a variety of manufacturing settings, but that also have toxic effects on fish. An experiment was conducted in which 140 fish eggs were available. Of the 140 eggs, 38 were chosen at random to be exposed to PCB Compound A, while 102 were chosen to be exposed to Compound B. The experiment focused on the number of eggs, for each compound, that eventually matured to become adult fish with deformities. For Compound A, 7 of the resulting adult fish had deformities; for Compound B, 32 of the adult fish had deformities. If pA represents the proportion of adult fish that have deformities resulting from Compound A, and similarly for pB , find a 99% confidence interval for pA − pB . Imagine using the confidence interval to examine the hypothesis: H0 : pA = pB . What conclusion might you draw regarding that hypothesis, and what limitations exist in terms of making that conclusion? 2. Gamma radiation has occasionally been suggested as a means by which foods could be rid of bacterial contaminents. To assess this, an experiment was conducted in which 17 petri plates were used. Each plate had a large colony of E. coli bacteria growing on it. Two different durations of radiation exposure were used: 30 seconds, or 2 minutes. Ten plates were randomly assigned to receive 30 seconds of exposure; the remainder received 2 minutes of exposure. After exposure, standard bacteriological methods were used to determine the number of surviving bacteria on the plates. The results are as follows: 30 seconds 0 0 1 5 6 8 13 15 29 64 2 minutes 0 2 3 4 7 9 12 (a) The researchers believe that these data do not come from normal distributions and they do not want to transform the data. Based on that, conduct a test of the null hypothesis that there is no difference between the treatments in terms of numbers of bacteria surviving, against the alternative that there is a difference between the treatments in terms of the numbers of bacteria surviving. (b) Below are normal scores plots for these two groups. Based on these plots, comment on the extent to which these data do or do not appear to come from normal distributions. - * 60+ - 30 sec - - - 40+ - - - * - 20+ - * - * - * * - * 0+ 2 * ------+---------+---------+---------+---------+---------+ -1.20 -0.60 0.00 0.60 1.20 1.80 2