Exercise Quiz 11

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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 Python:

	fit = smf.ols('Roughness ~ Supplier', data=D).fit()
	print(sm.stats.anova_lm(fit))

the following output is obtained: (wherein some of the values, however, has been replaced by the symbols A, B, C and D)

            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:

A = 4, B = 36, C = 28.72 and D = 3.11

A = 3, B = 32, C = 38.30 and D = 4.15

A = 36, B = 4, C = 3.19 and D = 0.35

A = 4, B = 36, C = 286.10 and D = 4.15

A = 3, B = 32, C = 286.10 and D = 31.00

Question 2 of 2

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

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 Python:

	fit = smf.ols('Roughness ~ Supplier', data=D).fit()
	print(sm.stats.anova_lm(fit))

the following output is obtained: (wherein some of the values, however, has been replaced by the symbols A, B, C and D)

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)

The roughness of the pipes does not depend on the selected supplier, as the P-value is less than 5%

The roughness of the pipes depends on the selected supplier, as the P-value is larger than 5%

The roughness of the pipes does not depend on the selected supplier, as the P-value is larger than 5%

The roughness of the pipes depends on the selected supplier, as the P-value is less than 5%

The roughness of the pipes does not depend on the selected supplier, since $114.89<295.33$