Question

The table to the right shows the cost per ounce​ (in dollars) for a random sample of toothpastes exhibiting very good stain​ removal, good stain​ removal, and fair stain removal. At alpha=0.05​, can you conclude that the mean costs per ounce are​ different? Perform a​ one-way ANOVA test by completing parts a through d. Assume that each sample is drawn from a normal​ population, that the samples are independent of each​ other, and that the populations have the same variances.

Very good stain removal   Good stain removal Fair stain removal
0.33 0.64 0.34
0.35 2.76 1.16
0.41 0.60 0.60
1.51 0.98  
0.48 0.75  
0.51 1.34  

​Critical Values F=3.89

Rejection region F > 3.89

(c.) Calculate the test statistic

Decide to reject or fail to reject the null hypothesis and interpret the decision in the context of the original claim.

Answer 1

We solve this problem using excel Data Analysis toolpack.

Excel => Data => Data Analysis => Anova : Single factor => select input range => Lables in first row => output range => ok

Very good stain removal	Good stain removal	Fair stain removal
0.33	0.64	0.34
0.35	2.76	1.16
0.41	0.6	0.6
1.51	0.98
0.48	0.75
0.51	1.34

k = number of group

N : total number of observation

Ho :  The mean costs per ounce are​ same.

V/s

H1: The mean costs per ounce are​ different

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
Very good stain removal	6	3.59	0.598333	0.204417
Good stain removal	6	7.07	1.178333	0.674977
Fair stain removal	3	2.1	0.7	0.1756

ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	1.094327	2	0.547163	1.382841	0.288115	3.885294
Within Groups	4.748167	12	0.395681
Total	5.842493	14

Here test stat = F = 1.3828

Critical value = Fc = 3.89

Here F = 1.3828 < Fc = 3.89 at 0.05 level of significance then we fail to reject Ho.

Conclude that  the mean costs per ounce are​ same.