3. Detergent manufacturers frequently make claims about the effectiveness of their products. A consumer-protection service decided to test the five best selling brands of detergent, where each manufacturer claims that its product produces the "whitest whites" in all water temperatures. The experiment was conducted in the following way. One hundred fifty white sheets were equally soiled. Thirty sheets were washed in each brand 10 with cold water, 10 with warm water, and 10 with hot water. After washing, the "whiteness" scores for each sheet were measured with laser equipment. Column A: Water temperature code Column B: Scores for detergent 1 (first 10 rows = cold water, middle 10 rows = warm, and last 10 rows = hot) Column C: Scores for detergent 2 (same format as column B) Column D: Scores for detergent 3 (same format as column B) Column E: Scores for detergent 4 (same format as column B) Column F: Scores for detergent 5 (same format as column B) a. What are the factors in this experiment? b. What is the response variable? c. Identify the levels of each factor. d. Perform a statistical analysis to determine whether there is sufficient statistical evidence to infer that there are differences in whiteness scores between the five detergents, differences in whiteness scores between the three water temperatures, or interaction between detergents and temperatures. Temperature Detergent1 Detergent2 Detergent3 Detergent4 Detergent5 Cold 66 83 70 44 84 Cold 87 62 75 59 67 Cold 55 61 62 47 99 Cold 41 85 68 60 85 Cold 68 75 72 79 73 Cold 49 78 92 62 74 Cold 52 68 70 73 76 Cold 57 66 71 64 82 Cold 66 93 74 69 79 Cold 62 81 80 81 79 Warm 78 63 71 70 87 Warm 65 47 88 80 100 Warm 68 88 90 78 83 Warm 75 74 85 72 82 Warm 57 71 78 71 93 Warm 48 71 69 75 76 Warm 84 71 60 101 87 Warm 69 68 80 81 76 Warm 55 80 61 87 70 Warm 78 68 89 84 78 Hot 99 82 97 85 84 Hot 87 85 98 83 95 Hot 57 72 79 94 82 Hot 84 71 60 89 74 Hot 93 72 84 77 97 Hot 64 77 58 100 87 Hot 90 73 79 92 80 Hot 85 88 86 102 76 Hot 64 75 91 93 91 Hot 84 77 75 86 96 Anova: Two-Factor With Replication SUMMARY Detergent1 Detergent2 Detergent3 Detergent4 Detergent5 Total Cold Count 10 10 10 10 10 Sum 603 752 734 638 798 50 3525 Average 60.3 75.2 73.4 63.8 79.8 70.5 Variance 160.9 114.177777 64.71111111 150.4 75.2888888 158.132653 Warm Count Sum 677 701 Average 67.7 70.1 Variance 133.788888 114.322222 FFF =7_ 771 799 77.1 79.9 128.1 86.7666666 79.2888888 134.530612 832 3780 83.2 75.6 Hot Count 10 10 10 10 10 50 Sum 807 772 807 901 862 4149 Average 80.7 77.2 80.7 90.1 86.2 82.98 Variance 196.9 35.0666666 188.011111159.21111111 69.7333333 122.224081 Total Count 30 Sum 2087 30 2225 30 2312 30 2338 30 2492 Average Variance 69.5666666 74.1666666 77.0666666 77.9333333 83.0666666 226.116092 91.0402298 127.374712 213.236781 76.6850574 ANOVA Source of Variation SS df MS Sample 3937.08 2 Columns 2967.42666 F P-value F crit 1968.54 17.8238028 0.00000013 3.06320385 4 741.856666 6.71701207 0.00005829 2.43873921 Interaction Within 2452.05333 14910 8 306.506666 2.77521126 0.00714047 2.00763499 135 110.444444 Total 24266.56 149