12. Toothpaste The table shows the costs per ounce (in dollars) for a sample of toothpastes...

12. Toothpaste The table shows the costs per ounce (in dollars) for a sample of toothpastes exhibiting very good stain removal, good stain removal, and fair stain removal. At α = 0.05, can you conclude that at least one mean cost per ounce is different from the others?

Using SPSS!!!

Very Good	.47	.49	.41	.37	.48	.51
Good	.60	.64	.58	.75	.46
Fair	.34	.46	.44	.60

Solutions

Expert Solution

The following table is obtained:

	Group 1	Group 2	Group 3
	0.47	0.6	0.34
	0.49	0.64	0.46
	0.41	0.58	0.44
	0.37	0.75	0.6
	0.48	0.46
	0.51

Sum =	2.73	3.03	1.84
Average =	0.455	0.606	0.46
∑iXij2	1.2565	1.8801	0.8808
St. Dev. =	0.054	0.105	0.107
SS =	0.01435	0.04392	0.0344
n =	6	5	4

The between sum of squares is computed directly as shown in the calculation below:

Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: μ1 = μ2 = μ3

Ha: At least one mean cost per ounce is different from the others

Conclusion

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that

at least one mean cost per ounce is different from the others at the α=0.05 significance level.

orchestra answered 1 year ago

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