1. **Problem Statement:** Analyze the factorial experiment data for yield based on pressure and temperature with three levels each and two replicates. 2. **Method:** Use two-factor factorial ANOVA to analyze main effects and interaction effects. 3. **Formula:** Total variation = Variation due to Pressure + Variation due to Temperature + Interaction + Error. 4. **Steps:** - Calculate means for each factor level and overall mean. - Compute sum of squares for Pressure (SS_P), Temperature (SS_T), Interaction (SS_PT), and Error (SS_E). - Calculate degrees of freedom for each source. - Compute mean squares (MS) by dividing SS by respective df. - Calculate F-statistics: $F_P = \frac{MS_P}{MS_E}$, $F_T = \frac{MS_T}{MS_E}$, $F_{PT} = \frac{MS_{PT}}{MS_E}$. - Compare F-values with critical F at $\alpha=0.05$ to determine significance. 5. **Interpretation:** Significant factors or interaction indicate influence on yield. 6. **Operating Conditions:** Choose pressure and temperature levels with highest mean yield and no significant negative interaction. --- 7. **Question 2:** Analyze influence of temperature and glass type on oscilloscope tube response. 8. **Method:** Two-factor factorial ANOVA with interaction. 9. **Steps:** - Calculate means and sum of squares for glass type, temperature, interaction, and error. - Compute F-statistics and compare with critical F at $\alpha=0.05$. - Determine if interaction or main effects are significant. 10. **Conclusion:** Significant interaction means effect of one factor depends on the other; otherwise, main effects are interpreted. --- 11. **Question 3:** Analyze two-factor factorial data and test for nonadditivity. 12. **Method:** Use Tukey's test for nonadditivity. 13. **Steps:** - Fit additive model and calculate residuals. - Compute test statistic for nonadditivity. - Compare with critical value at $\alpha=0.05$. 14. **Conclusion:** If nonadditivity is significant, interaction or nonlinear effects exist. **Final answers:** - Use factorial ANOVA for Questions 1 and 2 to identify significant factors and interactions. - Use Tukey's test for nonadditivity in Question 3. - Operate process at factor levels with highest yield and no significant negative interactions.