Name: ___________________________ INSTRUCTIONS: Answer the following problems. Copy relevant MS EXCEL outputs as solutions. For problems requiring test of hypotheses, provide appropriate conclusions. A. To ascertain the stability of vitamin C in reconstituted frozen orange juice concentrate stored in a refrigerator for a period of up to one week, the study Vitamin C Retention in Reconstituted Frozen Orange Juice was conducted by the Department of Human Nutrition and Foods at the Virginia Polytechnic Institute and State University. Three types of frozen orange juice concentrate: Richfood (R), Sealed-Sweet (S), and Minute Maid (M), were tested. The results, in milligrams of ascorbic acid per liter, were recorded as follows: Brand Amount of ascorbic acid per liter R 42.7 48.8 40.4 47.6 S 49.2 44.0 42.0 43.2 M 48.5 43.3 45.2 47.6 1. Is the assumption of equality of variance satisfied? Use a 5% level of significance. ANSWER: p-value=0.427709 2. Perform an appropriate test of hypothesis to determine if mean amount of ascorbic acid is the same for the three types of frozen orange juice tested. Use a 5% level of significance. ANSWER: p-value = 0.776196 B. The yields of wheat (in bushels per acre) were compared for five different varieties, A, B, C, D, and E, at six different locations. Each variety was randomly assigned to a plot at each location. The results of the experiment are shown in the accompanying table. VARIETY A 35.3 31.0 32.7 36.8 37.2 33.1 B 30.7 32.2 31.4 31.7 35 32.7 C 38.2 33.4 33.6 37.1 37.3 38.2 D 34.9 36.1 35.2 38.3 40.2 36 E 32.4 28.9 29.2 30.7 33.9 32.1 Assume that the population variances are equal. Use 5% level of significance. 1. Does the data provide sufficient evidence to indicate that the average yield varies among the five varieties of wheat? ANSWER: p-value=0.000198 2. Perform Tukey-Kramer procedure when necessary. Summarize the results. Use Q statistic = 4.15. C. In an experiment conducted to determine which of four different propellant types is preferable, the propellant burning rate for 24 static firings was measured. ANOVA results showed significant difference among the four different propellant types used. 1. Summarize the results of the post-hoc comparison conducted to determine the significantly different propellant type. Tukey Kramer Multiple Comparisons 1 2 3 4 Sample Mean 31.6 29.85 28.38333 28.53333 Other Data Level of significance Numerator d.f. Denominator d.f. MSW Q Statistic 0.05 4 20 2.579833 3.96 Group Absolute Std. Error Sampl e Size 6 6 6 6 Critical Comparison Group 1 to Group 2 Group 1 to Group 3 Group 1 to Group 4 Group 2 to Group 3 Group 2 to Group 4 Group 3 to Group 4 2. Difference 1.75 3.2166667 ____ ____ 1.3166667 0.15 of Difference 0.655722672 0.655722672 0.655722672 0.655722672 0.655722672 0.655722672 Range 2.5967 2.5967 2.5967 2.5967 2.5967 2.5967 Results Means are not different Means are different ____ ____ Means are not different Means are not different Which propellant type(s) are highly recommended? Suppose high burning rates are desired