4. An experiment was performed to assess the relative effects of five fertilizers on the yield...

 

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4. An experiment was performed to assess the relative effects of five fertilizers on the yield of a certain variety of sorghum. Five experimental plots were available at each of six locations throughout eastern Nebraska. The treatments were randomly assigned to the plots at each location. Yields of each plot were obtained at the end of the growing season. This experiment gave rise to 30 yield observations. a. Identify the 'treatments', 'blocks', experimental units, and sampling units in this experiment. Write out the linear model for this experiment. Be sure to identify all terms. b. Complete the following ANOVA table (assume locations are random effects): SOURCE MS Locations Total DF 5 29 SS 118.063 492.92 5437.23675 EMS c. Explain why the sorghum breeder would generally want to consider locations as random effects? (Hint: assume locations are considered to be a random sample of locations throughout eastern Nebraska.) d. At a = .05, use the appropriate F test to test the null hypothesis that there are no differences between the fertilizers with respect to population mean yield. Explain how you can use the expected mean squares to ensure your F test is testing the appropriate hypothesis. e. If fertilizer 4 had an average yield of 102 bu/ac, compute a 95% confidence interval for the difference between the population mean yields of fertilizer 4 and 5. State the EXACT meaning of this interval. (It is not acceptable to say you are 95% confident that ... ). f. If the yield of fertilizer 4 is slightly higher than fertilizer 5 at location 1 but is substantially below fertilizer 5 at location 3, what assumption of the randomized complete block design might be violated? 4. An experiment was performed to assess the relative effects of five fertilizers on the yield of a certain variety of sorghum. Five experimental plots were available at each of six locations throughout eastern Nebraska. The treatments were randomly assigned to the plots at each location. Yields of each plot were obtained at the end of the growing season. This experiment gave rise to 30 yield observations. a. Identify the 'treatments', 'blocks', experimental units, and sampling units in this experiment. Write out the linear model for this experiment. Be sure to identify all terms. b. Complete the following ANOVA table (assume locations are random effects): SOURCE MS Locations Total DF 5 29 SS 118.063 492.92 5437.23675 EMS c. Explain why the sorghum breeder would generally want to consider locations as random effects? (Hint: assume locations are considered to be a random sample of locations throughout eastern Nebraska.) d. At a = .05, use the appropriate F test to test the null hypothesis that there are no differences between the fertilizers with respect to population mean yield. Explain how you can use the expected mean squares to ensure your F test is testing the appropriate hypothesis. e. If fertilizer 4 had an average yield of 102 bu/ac, compute a 95% confidence interval for the difference between the population mean yields of fertilizer 4 and 5. State the EXACT meaning of this interval. (It is not acceptable to say you are 95% confident that ... ). f. If the yield of fertilizer 4 is slightly higher than fertilizer 5 at location 1 but is substantially below fertilizer 5 at location 3, what assumption of the randomized complete block design might be violated?

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a The treatments in this experiment are the five different fertilizers The blocks are the six locati... View the full answer