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Stat 509: Statistics for Engineers Homework Assignment 8 Make sure to include the R code and graphs used in your analyses. Fill out the following table: Table 1: ANOVA Table Df SS MS F p value Treatment 2 ? ? ? 0.0003 Residual ? 642.8 ? Total 31 1126.04 ? 1. How many groups must there be? 2. How many total subjects must there be? 3. What specific distribution does $\frac{MST}{MSE}$ have under the null hypothesis? 4. Do large or small values of F provide evidence against the null hypothesis? 5. This is the ANOVA table when testing whether the average miles per gallon (mpg) of a vehicle is dependent upon its number of forward gears (gear). Access the data by typing "attach(mtcars)" into R. Provide the R code which verifies your entries in the ANOVA rable. 6. State the null and alternative hypotheses in the context of this problem. $H_0$: $H_a$: 7. At the 0.001 significance level, is there evidence that the average mpg of a vehicle differs based upon its num- ber of forward gears? 8. Are the assumptions satisfied? 9. If necessary, perform a Tukey procedure at the 99.9% family-wise confidence level and explain all informa- tion it provides.

          Stat 509: Statistics for Engineers
Homework Assignment 8
Make sure to include the R code and graphs used in your analyses.
Fill out the following table:
Table 1: ANOVA Table
Df SS MS F p value
Treatment 2 ? ? ? 0.0003
Residual ? 642.8 ?
Total 31 1126.04 ?
1. How many groups must there be?
2. How many total subjects must there be?
3. What specific distribution does $\frac{MST}{MSE}$ have under the null hypothesis?
4. Do large or small values of F provide evidence against the null hypothesis?
5. This is the ANOVA table when testing whether the average miles per gallon (mpg) of a vehicle is dependent
upon its number of forward gears (gear). Access the data by typing "attach(mtcars)" into R.
Provide the R code which verifies your entries in the ANOVA rable.
6. State the null and alternative hypotheses in the context of this problem.
$H_0$:
$H_a$:
7. At the 0.001 significance level, is there evidence that the average mpg of a vehicle differs based upon its num-
ber of forward gears?
8. Are the assumptions satisfied?
9. If necessary, perform a Tukey procedure at the 99.9% family-wise confidence level and explain all informa-
tion it provides.

Stat 509: Statistics for Engineers
Homework Assignment 8
Make sure to include the R code and graphs used in your analyses.
Fill out the following table:
Table 1: ANOVA Table
Df SS MS F p value
Treatment 2 ? ? ? 0.0003
Residual ? 642.8 ?
Total 31 1126.04 ?
1. How many groups must there be?
2. How many total subjects must there be?
3. What specific distribution does (MST)/(MSE) have under the null hypothesis?
4. Do large or small values of F provide evidence against the null hypothesis?
5. This is the ANOVA table when testing whether the average miles per gallon (mpg) of a vehicle is dependent
upon its number of forward gears (gear). Access the data by typing "attach(mtcars)" into R.
Provide the R code which verifies your entries in the ANOVA rable.
6. State the null and alternative hypotheses in the context of this problem.
H0:
Ha:
7. At the 0.001 significance level, is there evidence that the average mpg of a vehicle differs based upon its num-
ber of forward gears?
8. Are the assumptions satisfied?
9. If necessary, perform a Tukey procedure at the 99.9% family-wise confidence level and explain all informa-
tion it provides.

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