Suppose that we want to compare the cleansing action of three detergents on the

Question

Suppose that we want to compare the cleansing action of three detergents on the basis of the following whiteness readings made on 15 swatches of white cloth, which were first soiled with India ink and then washed in an agitator-type machine with the respective detergents: Detergent A: 77 81 71 76 80 Detergent B: 72 58 74 66 70 Detergent C: 76 85 82 77 80 The means of these three samples are 77, 68, and 80, determine whether the differences among them are significant for alpha = 0.01. Use Tukey's test at alpha = 0.02 to determine the nature of the differences among treatment means.

Explanation / Answer

Answer:

H_0: mu_1 = mu_2= mu_3

H1: At least one pair of population means are different

Table value of F with (DF1=2, DF2=12 ) at 0.01 level =6.93

Calculated F=8.48 >6.93 the table value

The null hypothesis is rejected.

The data indicate there is a significant difference among the three groups

One-way ANOVA: A, B, C

Method

Null hypothesis         All means are equal

Alternative hypothesis At least one mean is different

Significance level      = 0.05

Equal variances were assumed for the analysis.

Factor Information

Factor Levels Values

Factor       3 A, B, C

Analysis of Variance

Source DF Adj SS Adj MS F-Value P-Value

Factor   2   390.0 195.00     8.48    0.005

Error   12   276.0   23.00

Total   14   666.0

Model Summary

      S    R-sq R-sq(adj) R-sq(pred)

4.79583 58.56%     51.65%      35.25%

Means

Factor N   Mean StDev      95% CI

A       5 77.00   3.94 (72.33, 81.67)

B       5 68.00   6.32 (63.33, 72.67)

C       5 80.00   3.67 (75.33, 84.67)

Pooled StDev = 4.79583

Tukey Pairwise Comparisons

Grouping Information Using the Tukey Method and 98% Confidence

Factor N   Mean Grouping

C       5 80.00 A

A       5 77.00 A B

B       5 68.00    B

Means that do not share a letter are significantly different.

Tukey Simultaneous Tests for Differences of Means

Difference Difference       SE of                            Adjusted

of Levels     of Means Difference       98% CI      T-Value   P-Value

B - A            -9.00        3.03 (-18.65, 0.65)    -2.97     0.029

C - A             3.00        3.03 ( -6.65, 12.65)     0.99     0.597

C - B            12.00        3.03 ( 2.35, 21.65)     3.96     0.005

Individual confidence level = 99.21%

b).

Tukey test shows that detergent B and C are significant at 0.02 level significance.

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