Question: c) Interaction Between Air Temperature and Supplement Dose To determine if the effect of Air Temperature on Body Temperature depends on the supplement dose, we
c) Interaction Between Air Temperature and Supplement Dose To determine if the effect of Air Temperature on Body Temperature depends on the supplement dose, we need to examine the interaction term between Air Temperature and Dose (Air TempDose) in the ANOVA table. Given: Type 1 SS for Air TempDose = 0.2616 Total SS = 0.0246 + 0.0000 + 0.1158 + 0.1596 + 0.2616 + 2.1845 = 2.7461 Calculating the degrees of freedom for the interaction term. df_Interaction = 2 (given in the question) Calculating the Mean Square (MS) for the interaction term. MS_Interaction = Type 1 SS_Interaction / df_Interaction MS_Interaction = 0.2616 / 2 = 0.1308 Calculating the Mean Square Error (MSE) from the ANOVA table. MSE = SS_Error / df_Error df_Error = Total number of observations - Total number of parameters df_Error = 125 - (1 + 1 + 1 + 2 + 3 + 2) = 115 MSE = 2.1845 / 115 = 0.0190 Calculating the F-statistic for the interaction term. F_Interaction = MS_Interaction / MSE F_Interaction = 0.1308 / 0.0190 = 6.88 Determine the p-value for the F-statistic. The F-statistic follows an F-distribution with (df_Interaction, df_Error) degrees of freedom. p-value = P(F(2, 115) > 6.88) Using an F-distribution table, we can find the p-value is 0.0015. Interpretation: At the 0.05 significance level, there is strong evidence to conclude that the effect of Air Temperature on Body Temperature depends on the supplement dose (p-value = 0.0015 < 0.05). The significant interaction term suggests that the re
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