Question 7.2: The article "Effect of Welding Procedure on Flux Cored Steel...
The article “Effect of Welding Procedure on Flux Cored Steel Wire Deposits” (N. Ramini de Rissone, I. deS. Bott, et al., Science and Technology of Welding and Joining, 2003: 113- 122) compares properties of welds made using carbon dioxide as a shielding gas with those of welds made using a mixture of argon and carbon dioxide. One property studied was the diameter of inclusions, which are particles embedded in the weld. A sample of 544 inclusions in welds made using argon shielding averaged 0.37 μm in diameter, with a standard deviation of 0.25 μm. A sample of 581 inclusions in welds made using carbon dioxide shielding averaged 0.40 μm in diameter, with a standard deviation of 0.26 μm. (Standard deviations were estimated from a graph.) Can you conclude that the mean diameters of inclusions differ between the two shielding gases?
Let \bar{X}=0.37 denote the sample mean diameter for argon welds. Then s_X = 0.25 and the sample size is n_X=544. Let \bar{Y}=0.37 denote the sample mean diameter for carbon dioxide welds. Then s_Y = 0.26 and the sample size is n_Y = 581. Let μ_X denote the population mean diameter for carbon dioxide welds. The null and alternate hypotheses are
H_0: \mu_X-\mu_Y=0\quad \text{versus}\quad H_1: \mu_X-\mu_Y \neq 0
The value of the test statistic is
z=\frac{0.37-0.40-0}{\sqrt{0.25^2 / 544+0.26^2 / 581}}=-1.97
This is a two-tailed test, and the P -value is 0.0488 (see Figure 7.2). A follower of the 5% rule would reject the null hypothesis. It is certainly reasonable to be skeptical about the truth of H_0 .
