Artificial Teeth: wear. In a study by J. Zeng et al., three materials for making artificial teeth-Endura, Duradent and Duracross-were tested for wear. Their results were published as the paper "In Vitro Wear Resistance of Three Types of Composite Resin Denture Teeth" (Journal of Prosthetic Dentistry, Vol. $94$, Issue $5$, pp. $453-$$457)$. Using a machine that stimulated grinding by two right first molars at $60$strokes per minute for a total of $50,000$strokes, the researchers measured the volume of material worn away, in cubic millimeters. Six pairs site of teeth were tested for each material. The data on the WeissStats site are based on the results obtained by the researchers. At the $5\%$significance level, do the data provide sufficient evidence to conclude that there is a difference in mean wear among the three materials?

a.

Examine whether the figures provide enough evidence to prove that the three materials have distinct mean wear rates.

It is necessary to state the null and alternative hypotheses.

Null Hypothesis:

$H_0:{\mu }_{Northeast}={\mu }_{Reduced}={\mu }_{Control}={\mu }_{Enlarged}$

Alternative hypothesis:

$H_a$: A minimum of one ${\mu }_1$in comparison to others.

That is, the data is sufficient to determine whether the three materials have distinct average wear rates.

The importance level here is, $\alpha =0.005$

Calculate the value of the test statistic:

MINITAB procedures:

Step 1: Select Stat > ANOVA > One-Way Analysis from the menu bar.

Step 2:Enter the Volume column in the Response column.

Step 3: Enter the Material column in Factor.

Step 4: Press the OK key.

One-way ANOVA on volume vs. material

Source DF SS MS F P

MATERIAL $2$ $2.02446$ $1.01223$ $341.16$ $0.000$

Error $15$ $0.04450$ $0.00297$

Total $17$ $2.06896$

$s=0.05447$ $R-Sq=97.85\%$ $R-Sq\left(adj\right)=97.56\%$

Level N Mean StDev

Duracross $6$ $0.22000$ $0.08000$

Duradent $6$ $0.87000$ $0.03000$

Endura $6$ $0.10998$ $0.04002$

Pooled StDev $=0.05447$

The value of F is $341.16$ and the p-value is $0.000$, according to the MINITAB output.

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