# Engineering Statistics Data Analysis

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Engineering Statistics         Homework                  Fall 2015

Submit a written report with the answers for the following problem. Use a wordprocessor for the report and Minitab for conducting the statistical analysis (number the pages)

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, l0 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. Use data set detergent.xls on blackboard to answer the following

1. Compare box plots for each treatment. What comments (about the populations) do you have from examining these plots.

[pic 3][pic 2]

Therefore, Detergent 1 has large variance in five of detergents; its mean for the cold experiment tends to be really small. Detergent 2 has small variance, 3 experiments may have same mean. Detergent 3 has small variance for cold experiment while detergent 4 has small variance for hot. In general, all 5 detergents may have same mean. Other than detergent 1, 2345 may have same variance.

1. Obtain residuals from the ANOVA test (do not make conclusions about the ANOVA test until assumptions are verified).

FITS         RESI

1        66        60.3        5.7

1        87        60.3        26.7

1        55        60.3        -5.3

1        41        60.3        -19.3

1        68        60.3        7.7

1        49        60.3        -11.3

1        52        60.3        -8.3

1        57        60.3        -3.3

1        66        60.3        5.7

1        62        60.3        1.7

1        78        67.7        10.3

1        65        67.7        -2.7

1        68        67.7        0.3

1        75        67.7        7.3

1        57        67.7        -10.7

1        48        67.7        -19.7

1        84        67.7        16.3

1        69        67.7        1.3

1        55        67.7        -12.7

1        78        67.7        10.3

1        99        80.7        18.3

1        87        80.7        6.3

1        57        80.7        -23.7

1        84        80.7        3.3

1        93        80.7        12.3

1        64        80.7        -16.7

1        90        80.7        9.3

1        85        80.7        4.3

1        64        80.7        -16.7

1        84        80.7        3.3

2        83        75.2        7.8

2        62        75.2        -13.2

2        61        75.2        -14.2

2        85        75.2        9.8

2        75        75.2        -0.2

2        78        75.2        2.8

2        68        75.2        -7.2

2        66        75.2        -9.2

2        93        75.2        17.8

2        81        75.2        5.8

2        63        70.1        -7.1

2        47        70.1        -23.1

2        88        70.1        17.9

2        74        70.1        3.9

2        71        70.1        0.9

2        71        70.1        0.9

2        71        70.1        0.9

2        68        70.1        -2.1

2        80        70.1        9.9

2        68        70.1        -2.1

2        82        77.2        4.8

2        85        77.2        7.8

2        72        77.2        -5.2

2        71        77.2        -6.2

2        72        77.2        -5.2

2        77        77.2        -0.2

2        73        77.2        -4.2

2        88        77.2        10.8

2        75        77.2        -2.2

2        77        77.2        -0.2

3        70        73.4        -3.4

3        75        73.4        1.6

3        62        73.4        -11.4

3        68        73.4        -5.4

3        72        73.4        -1.4

3        92        73.4        18.6

3        70        73.4        -3.4

3        71        73.4        -2.4

3        74        73.4        0.6

3        80        73.4        6.6

3        71        77.1        -6.1

3        88        77.1        10.9

3        90        77.1        12.9

3        85        77.1        7.9

3        78        77.1        0.9

3        69        77.1        -8.1

3        60        77.1        -17.1

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