Question

1. A consumer research organization was interested in the influence of type of water on the effectiveness of a detergent. Test batches of washings were run in four randomly chosen machines having a particular type of water - soft, moderate, and hard. All batches had equal numbers of oil- stained rags and after each washing the number of rags stilled stained was determined. The following results were obtained. Number of Rags with Stains Sample Observations Soft Moderate Hard 1 0 4 10 2 1 8 5 3 2 3 7 4 1 5 10 Using an alpha level of .01, would you conclude that the type of water influences the effectiveness of the detergent? HTML Editor

Make sure that include any excel solutions. Be sure that have hypotheses with various test.

Please really need help!

NO need to attached the excel just show the work and

any excel solutions. Be sure that have hypotheses with various test.

Answer 1

Basically, we need to know if the mean across these three categories is equal or not. Below are the hypothesis that we test:

HO: M1 = 42 = 43

H:He is not true

The Analysis of Variance (ANOVA) test is performed and below is the excel output which was obtained using data analysis toolpak

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
Soft	4	4	1	0.666666667
Moderate	4	20	5	4.666666667
Hard	4	32	8	6
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	98.67	2	49.33	13.059	0.002	8.022
Within Groups	34	9	3.78
Total	132.6666667	11

The P-value is 0.002 which is less than alpha of 0.01. Hence, we may reject the null hypothesis that means are equal across categories.

в со G H 4 Count 4 4 4 Sum 4 20 32 Average Variance 1 0.666666667 5 4.666666667 1 Anova: Single Factor 2 3 SUMMARY Groups 5 Soft 6 Moderate 7 Hard 8 9 10 ANOVA 11 Source of Variation 12 Between Groups 13 Within Groups 14 15 Total 16 F SS df 98.67 2 34 9 MS 49.33 3 .78 P 13.059 3.059 P-valuecoa -value 0.002 F crit 8.022 Feries 132.6666667 11