In a weld experiment, the hardness measurements were made for five welds from ea

Question

In a weld experiment, the hardness measurements were made for five welds from each of four fluxes, A, B, C, and D. The sample mean hardness values were X_A. = 252.2, X_B. = 260.2, X_C. = 273.8, and X_D. = 262.8. The MSE was 33.58. Before the experiment was performed, the carbon contents of the fluxes were measured. Flux B had the lowest carbon content (2.67% by weight), and flux C had the highest (5.05% by weight). The experimenter is therefore particularly interested in comparing the harnesses obtained with these two fluxes. Find a 95% confidence interval for the difference in mean hardness between welds produced with flux B and those produced with flux C. Can we conclude that the two means differ? A. We can conclude that the treatment means differ. B. We cannot conclude that the treatment means differ.

Explanation / Answer

xA= 252.2 ; xB = 260.2 ; xC = 273.8 ; xD= 262.8

So we will measure it with Tukey HSD post hoc test

Here Q = (Mmax-  Mmin)/sqrt [MSE/n]

Here Mmax = 273.8 and   Mmin= 260.2 ; MSE = 33.58 and n = 5

Q = (273.8 - 260.2)/ sqrt [33.58/5] = 13.6/ 2.5915 = 5.248

If we look into critical Q - value table for dF = 4 * (5-1) = 16 and number of treatments = 4 and alpha = 0.05

Qcritical = 4.046

so here Q > Qcritical

so we can say that there is significant difference between both treatment means.

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.