Question

For #8 on page 469, put the data in Excel with the correct format for ANOVA. See the page 22 on ANOVA 1 slide. Then do Levene test and write down the p-value of Levene test with 3 decimal points.

8. FILE Detergent. A well-known conglomerate claims that its detergent "whitens and brightens better than all the rest." In order to compare the cleansing action of the top three brands of detergents, 24 swatches of white cloth were soiled with red wine and grass stains and then washed in front-loading machines with the respective detergents. The following whiteness readings were obtained: Detergent 2 1 3 84 78 87 79 74 80 87 81 91 85 86 77 86 78 94 89 89 79 89 69 77 83 79 78

Answer 1

The Data

Detergent 1	Detergent 2	Detergent 3
84	78	87
79	74	80
87	81	91
85	86	77
94	86	78
89	89	79
89	69	77
83	79	78

The tests

Method

Null hypothesis   All variances are equal
Alternative hypothesis   At least one variance is different
Significance level   α = 0.05

95% Bonferroni Confidence Intervals for Standard Deviations

Sample N   StDev CI
Detergent 1 8 4.55914   (2.24810, 13.1943)
Detergent 2 8   6.71353   (3.48027, 18.4809)
Detergent 3 8   5.22186   (1.40284, 27.7382)
Individual confidence level = 98.3333%

Tests

Method Test Statistic   P-Value
Multiple comparisons   — 0.566
Levene 0.64 0.537

Note: Used Minitab for calcutation