Question

The production manager thinks that the humidity is affecting the production rate as it increases. Using an alpha of 5% determine if humidity affects the rate of production.

Temperature 70 90 80 125 130 132 125 118 124 Shift 1 137 141 142 Shift 2 140 138 136

Determine:

⦁ The Sum of Square for total variation

⦁ The Sum of Square for the treatment

⦁ The Sum of Square for the block

⦁ The Sum of Square for the intersection of block and treatment

⦁ The Sum of Square for the experiment errors

⦁ The Experimental F Temperature

⦁ The Experimental F Shifts

⦁ The Experimental F Temperature and Shifts

⦁ The Critical Value of F Temperature

⦁ The Critical Value of F Shifts

⦁ The Critical Value of F Temperature and Shifts

⦁ Based on the ANOVA: what conclusion should be taken for Temperature:

-Significant impact for the temperature and shifts

-Significant impact for the temperature

-No significant impact of the temperature

-None of the above

⦁ Based on the ANOVA: what conclusion should be taken for shifts:

-Significant impact for the temperature and shifts

-Significant impact for the shifts

-No significant impact of the shifts

-None of the above

⦁ Based on the ANOVA: what conclusion should be taken for both:

-Significant impact for the temperature and shifts

-Significant impact for the temperature only

-No significant impact of the temperature and shifts

-None of the above

Answer 1

By using MINITAB,

MTB > GLM;
SUBC> Response 'responce';
SUBC> Nodefault;
SUBC> Categorical 'Temperature' - 'shift';
SUBC> Terms Temperature shift;
SUBC> TMethod;
SUBC> TAnova;
SUBC> TFactor.

General Linear Model: responce versus Temperature, shift

Factor Information

Factor Type Levels Values
Temperature Fixed 3 70, 80, 90
shift Fixed 2 1, 2

Analysis of Variance

Source DF Adj SS Adj MS F-Value P-Value
Temperature 2 8.167 4.083 0.19 0.834
shift 1 533.333 533.333 24.43 0.003
Temperature*shift 2 10.167 5.083 0.23 0.799
Error 6 131.000 21.833
Total 11 682.667

The Critical Value of F Temperature = F_{(df temperature , df error)} = F_(2,6) = 5.14

The Critical Value of F Shifts = F_{(df shifts , df error)} = F_(1,6)  = 5.99

The Critical Value of F Temperature and Shifts =  F_{(df temperature*shifts , df error)} = F_(2,6) = 5.14

From pvalue (Temperature) =0.834 > alpha = 0.05

Accept H0. No significant impact on Temperature.

From pvalue (Shifts) =0.003 < alpha = 0.05

Reject H0, Significant impact for the shifts

From pvalue (Temperature * Shifts) =0.799 > alpha = 0.05

Accept H0. No significant impact of the temperature and shifts.