An aluminum producer manufactures carbon anodes and bakes them in a ring furnace

Question

An aluminum producer manufactures carbon anodes and bakes them in a ring furnace prior to use in the smelting operation. The baked density of the anode is an important quality characteristic, as it may affect anode life. One of the process engineers suspects that firing temperature in the ring furnace affects baked anode density. An experiment was run at four different temperature levels, and six anodes were baked at each temperature level. The data from the experiment are shown in the Table below-

(a) What statistical technique was used? Justify the statistical technique used.

(b) State the null and alternative hypothesis.

(c) Does firing temperature in the ring furnace affect mean baked anode density? Explain how you came to this conclusion.

(d) What conclusion can be drawn from the residual plots? Why do we need to do this?

(e) Comment on the box-plot and compare to your conclusion in (c).

(f) What firing temperature would you recommend using?

Table 2- Baked Density Data Temp (CC) 500 525 550 575 Density 41.8 41.941.741.6 41.541.7 41.4 41.3 41.741.641.741.8 41.2 41.041.641.941.741.3 41.0 40.641.841.241.9 41.5 MINITAB OUTPUT (for Part MTB > Stat> ANOVA > One-Way One-way ANOVA F naaa5 0.152 1.4 Source R..ssMS Source DES 3wa.A5Z 0.152 1.45 0.258 Rxxai 2.097 0.105 Total2.553 S = 0.3238 R-Sa= 17.89% R-Saadi)= 5.57% Individual 95% CIs For Mean Based on Pooled StDev Level N 500 525 550 575 Mean StDev -_- 6 41.700 0.141 6 41.583 0.194 6 41.450 0.339 6 41.333 0.497 (- 41.25 41.50 41.75 42.00 Pooled StDev = 0.324

Explanation / Answer

(a) one-way ANOVA was used because there are more that 2 groups to compare.

(b) Null: Mean baked anode density at all temperatures are same.

Alternative: At least at one temperature, mean baked anode density is different from others.

(c) since p-value is greater than 0.05, we can conclude that firing temperature in the ring furnace does not affect mean baked anode density.

(d) residual plot shows that residuals are normally distributed.

(e) Box-plot shows that as temperature increases, variability also increases.

(f) I would recomment 500 because at this temperatiure, variability is minimum.

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