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Problem 3: A consumer group is attempting to find whether there is a difference between three brands of flower seeds. The variable recorded is the number of seeds, out of 100 which sprouted. Six packages of seeds were used for each brand. At the .05 level is there a difference between brands? Brand 3 Brand 2 Brand 1 a) Identify the hypotheses. M M M 32 Ho: B1-B2-B, 1-V H: Ther is Betten a the differene Trands: at least I mean differs C b) Calculate the mean number that sprouted for each brand Brandi B, Brande Br Brand Bz. 566.50 X 56.17 = 85.83 X c) Fill in the ANOVA table. P-value Source Factor ssd 272.33 2 51 29.17 15 7850. 5 17 MSF 1360.665 3.972 341.945 – – 0,411 Error Total d) state your decision and conclusion. Provide justification therefore. P-vawe so.05 there ise diffrence between the brands-
Problem 3 continued). We now wish to perform post-hoc multiple- comparison tests on the data from the previous page. e) Each of the Fisher confidence intervals should have the same margin of error. Explain why this is the case. Seme each of the fisher confidence intervals have that margin of error because they have the same lool sempre rices and we are comparing all of them with 6 packages of seeds so the margin D of error should be 957 f) Find the critical value and the standard error of the difference between means and use them to state the margin of error. G re 2.11 14.492) Critical value : 2.11 W rowy or the same for the CI 95% magnol enor – 2.11(18.692) (0577) = 22.5134 g) Use your answers from part band to compute the 95 Fisher confidence interval for each combination means. u 22.5134 + 85.83 = 108.34 27.134 + 66.50 = 89.01 works! 22.5134 +56-17 S 78.68 h) Which brands display significant differences between each other? How can you tell? brand I and 2
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