5. A doctor was interested in determining if there was a difference in the mean length of time required to recover from COVID-19 for people in their 20's, 30's, 40's, 50's, and 60+. To see whether these people differ in their recovery time, one person in each age group was selected from each of 5 different ethnic groups, and the recovery time following infection with COVID-19 for each person was recorded. a. (5 points) Explain why a randomized block experiment (with blocks corresponding to the 5 different ethnic groups) was used rather than a one-way ANOVA experiment. b. (10 points) The accompanying table is a partially completed ANOVA table for the randomized block design experiment described above. Fill in the table and use that information to test the null hypothesis of no difference in the mean recovery time for people in the 5 different age groups. Use a 0.05 level of significance. Source of Degrees of Sum of Mean F Variation Freedom Squares Square Treatment 117.3 Block 1123.7 Error Total 1429.5 c. (5 points) The accompanying table is a partially completed ANOVA table for a One-Way ANOVA test based on the situation above. Fill in the table. (HINT: Think about how One-Way ANOVA relates to RBD ANOVA). Degrees of Freedom Sum of Squares Mean Square F Source of Variation Treatment Error Total 1439.5 5. A doctor was interested in determining if there was a difference in the mean length of time required to recover from COVID-19 for people in their 20's, 30's, 40's, 50's, and 60+. To see whether these people differ in their recovery time, one person in each age group was selected from each of 5 different ethnic groups, and the recovery time following infection with COVID-19 for each person was recorded. a. (5 points) Explain why a randomized block experiment (with blocks corresponding to the 5 different ethnic groups) was used rather than a one-way ANOVA experiment. b. (10 points) The accompanying table is a partially completed ANOVA table for the randomized block design experiment described above. Fill in the table and use that information to test the null hypothesis of no difference in the mean recovery time for people in the 5 different age groups. Use a 0.05 level of significance. Source of Degrees of Sum of Mean F Variation Freedom Squares Square Treatment 117.3 Block 1123.7 Error Total 1429.5 c. (5 points) The accompanying table is a partially completed ANOVA table for a One-Way ANOVA test based on the situation above. Fill in the table. (HINT: Think about how One-Way ANOVA relates to RBD ANOVA). Degrees of Freedom Sum of Squares Mean Square F Source of Variation Treatment Error Total 1439.5
