1. An experiment was conducted to study the time (in minutes) it takes to cook rice...

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1. An experiment was conducted to study the time (in minutes) it takes to cook rice in a cooker that has an inner water area and an outer water area. Four factors were considered: amount of rice (1 cup versus 2 cups); amount of inner water (2 cups versus 3 cups); amount of outer water (0.5 cup versus 1 cup); and type of rice (short grain versus long grain). In order to save efforts, a researcher performed a fractional factorial design and conducted the eight experiments with results listed in the table below: Inner water Rice (cups) Outside water Type of rice (cups) Cooking time (minutes) 1 2 0.5 Short 26.4 2 3 0.5 Short 28.9 2 2 1.0 Short 28.4 2 2 0.5 Long 27.1 1 3 1.0 Short 30.1 3 0.5 Long 28.6 1 2 1.0 Long 27.9 2 3 1.0 Long 31.5 (a) Please use the knowledge learned from class to determine whether the researcher did a correct job on fractional factorial design. (/1) (b) Compute the average effect for each of the four main effects and the interaction effects. (/2) (c) Set up a normal probability plot of the average effects. (/2) (d) Given the results of (c), combine all appropriate effects with less influence into a measure of random error based on your own judgement, and, using the level of significance 0.05, determine which factors are significant. (/2) (e) Justify your choices based on ANOVA analysis. (/3) 1. An experiment was conducted to study the time (in minutes) it takes to cook rice in a cooker that has an inner water area and an outer water area. Four factors were considered: amount of rice (1 cup versus 2 cups); amount of inner water (2 cups versus 3 cups); amount of outer water (0.5 cup versus 1 cup); and type of rice (short grain versus long grain). In order to save efforts, a researcher performed a fractional factorial design and conducted the eight experiments with results listed in the table below: Inner water Rice (cups) Outside water Type of rice (cups) Cooking time (minutes) 1 2 0.5 Short 26.4 2 3 0.5 Short 28.9 2 2 1.0 Short 28.4 2 2 0.5 Long 27.1 1 3 1.0 Short 30.1 3 0.5 Long 28.6 1 2 1.0 Long 27.9 2 3 1.0 Long 31.5 (a) Please use the knowledge learned from class to determine whether the researcher did a correct job on fractional factorial design. (/1) (b) Compute the average effect for each of the four main effects and the interaction effects. (/2) (c) Set up a normal probability plot of the average effects. (/2) (d) Given the results of (c), combine all appropriate effects with less influence into a measure of random error based on your own judgement, and, using the level of significance 0.05, determine which factors are significant. (/2) (e) Justify your choices based on ANOVA analysis. (/3)