1. An experiment was conducted to study the time (in minutes) it takes to cook rice in a cooker thathas an inner water area and an outer water area. Four factors were considered: amount of rice (1cup versus 2 cups); amount of inner water (2 cups versus 3 cups); amount of outer water (0.5 cupversus 1 cup); and type of rice (short grain versus long grain). In order to save efforts, aresearcher performed a fractional factorial design and conducted the eight experiments withresultslistedinthetable below:

Rice(cups)	Inner water(cups)	Outsidewater	Typeof rice	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
1	3	0.5	Long	28.6
1	2	1.0	Long	27.9
2	3	1.0	Long	31.5

1. Pleaseusetheknowledgelearnedfromclasstodeterminewhethertheresearcherdidacorrectjobonfractionalfactorialdesign.(/1)
2. Computetheaverage effectforeachofthe four maineffectsandtheinteractioneffects.(/2)
3. Set upanormalprobabilityplotoftheaverageeffects.(/2)
4. Given the results of (c), combine all appropriate effects with less influence into a measure ofrandom error based on your own judgement, and, using the level of significance 0.05, determinewhichfactors are significant.(/2)
5. JustifyyourchoicesbasedonANOVAanalysis (/3).