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## Question 1 of 2

A company is going to use some pipes. It is essential for the use that the interior pipe roughness is minimized. To find the most suitable supplier of pipes, samples of pipes are obtained from four potential suppliers. From each supplier a sample of 9 pipes were taken and measurements of the interior pipe roughness are taken. The measurement data is shown in the following table: (Roughness in $\mu$m)

Supplier                   $\bar{x}$ in $\mu$m $s$ in $\mu$m
1 17 25 22 21 16 22 23 20 17 20.3 3.08
2 21 25 20 19 24 19 21 21 17 20.8 2.49
3 14 13 16 16 17 24 20 15 19 17.1 3.41
4 18 19 20 12 13 19 20 14 17 16.9 3.10

A one-way analysis of variance was run in R:

	anova(lm(Roughness~Supplier))


the following output is obtained: (wherein some of the values, however, has been replaced by the symbols A, B, C and D)

Analysis of Variance Table

Response: Roughness
Df  Sum Sq   Mean Sq    F value     Pr(>F)
Supplier     A  114.89      C           D       0.01363
Residuals    B  295.33    9.229


The values for A, B, C and D are:

## Question 2 of 2

If you did the previous exercise, the following is a repetition:

A company is going to use some pipes. It is essential for the use that the interior pipe roughness is minimized. To find the most suitable supplier of pipes, samples of pipes are obtained from four potential suppliers. From each supplier a sample of 9 pipes were taken and measurements of the interior pipe roughness are taken. The measurement data is shown in the following table: (Roughness in $\mu$m)

Supplier                   $\bar{x}$ in $\mu$m $s$ in $\mu$m
1 17 25 22 21 16 22 23 20 17 20.3 3.08
2 21 25 20 19 24 19 21 21 17 20.8 2.49
3 14 13 16 16 17 24 20 15 19 17.1 3.41
4 18 19 20 12 13 19 20 14 17 16.9 3.10

A one-way analysis of variance was run in R:

	anova(lm(Roughness~Supplier))


the following output is obtained: (wherein some of the values, however, has been replaced by the symbols A, B, C and D)

Analysis of Variance Table

Response: Roughness
Df  Sum Sq   Mean Sq    F value     Pr(>F)
Supplier     A  114.89      C           D       0.01363
Residuals    B  295.33    9.229


If we test on a 5\% level of significance, the result of the hypothesis test for whether roughness of the pipes depend on the selected supplier is: (both the conclusion and reasoning must be right)