3.30. Several ovens in a metal working shop are used to heat metal specimens. Al

Question

3.30. Several ovens in a metal working shop are used to heat metal specimens. All the ovens are supposed to operate at the same temperature, although it is suspected that this may not be true. Three ovens are selected at random, and their tem- peratures on successive heats are noted. The data collected are as follows: Oven Temperature 1491.50 498.30 498.10 493.50 493.60 2 488.50 484.65 479.90 477.35 3 490.10 484.80 488.25 473.00 471.85 478.65 (a) Is there significant variation in temperature between ovens? Use 0.05. (b) Estimate the components of variance for this model. (c) Analyze the residuals from this experiment and draw conclusions about model adequacy

Explanation / Answer

Given data is a table as shown in question

Ti = total for each row

ni= no of elements in each row

S.S = sum of squares of each element

Null hypothesis: All the treatments are not significant

Alternate hypothesis: Treatments have significant difference

Total S.S =

Q = S.S - T^2/N = 3545941.223 - 7292^2/15

= 1056.956

Q1 = Ti^2/ni - T^2/N

=  3545527 - 7292^2/15

= 642.733

Q2 = Q - Q1

= 414.233

Constructing the one side ANOVA table

Critical value of F at df (2.13) at 95% C.I is 3.8553

Since critical value is less than calculated value, we, therefore, conclude that alternate hypothesis is correct

Oven Ti Ti^2 ni Ti^2/ni Sum of squares 1 491.5 498.3 498.1 493.5 493.6 2475 6125625 5 1225125 1225161.96 2 488.5 484.65 479.9 477.35 1930.4 3726444 4 931611 931684.905 3 490.1 484.8 488.25 473 471.85 478.65 2886.65 8332748 6 1388791 1389094.358 TOTAL 7292.05 18184817 15 3545527 3545941.223

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