A statistical program is recommended. According to an article the submerged arc welding (SAW) process is commonly used for joining thick plates and pipes. The heat affected zone (HAZ), a band created within the base metal during welding, was of particular interest to the investigators. Here are observations on depth (mm) of the HAZ both when the current setting was high and when it was lower. Non-high 1.03 1.13 1.26 1.69 1.89
1.97 2.34 2.47 2.69
1.38 1.42 1.55 1.74 1.91
2.06 2.57 2.65 2.83
High 1.57 2.03 2.00 2.03 2.36
2.56 2.95 2.96 2.98
(A) Comment on interesting features.
a) According to the boxplots, depth measurements are generally somewhat larger when the current is set at the lower current setting than at the higher current setting.
b) According to the boxplots, depth measurements are generally the same at both levels of current setting.
c) According to the boxplots, depth measurements are generally somewhat larger when the current is set at the higher current setting than at the lower current setting.
d) According to the boxplots, there appear to be multiple outliers in the depth measurements when the current is set at the higher current setting.
e) According to the boxplots, there appear to be multiple outliers in the depth measurements when the current is set at the lower current setting.
(B) Is it reasonable to use the two-sample t test to test hypotheses about the difference between true average HAZ depths for the two conditions?
a) No. A normal probability plot of the differences is noticeably non-linear and so it is not plausible that the difference population is normal.
b) Yes. The measurements are all positive so it is at least plausible that the difference population is normal.
c) No. A normal probability plot of the differences is reasonably linear and so it is not plausible that the difference population is normal.
d) Yes. A normal probability plot of the differences is noticeably non-linear and so it is at least plausible that the difference population is normal.
e) Yes. A normal probability plot of the differences is reasonably linear and so it is at least plausible that the difference population is normal.
(C) Does it appear that true average HAZ depth is larger for the higher current condition than for the lower condition? Carry out a test of appropriate hypotheses using a significance level of 0.01. (Use μ1 for the higher current condition and μ2 for the lower current condition.)
State the relevant hypotheses.
a) H0: μ1 − μ2 > 0
Ha: μ1 − μ2 = 0
b) H0: μ1 − μ2 = 0
Ha: μ1 − μ2 ≠ 0
c) H0: μ1 − μ2 < 0
Ha: μ1 − μ2 = 0
d) H0: μ1 − μ2 = 0
Ha: μ1 − μ2 < 0
e) H0: μ1 − μ2 = 0
Ha: μ1 − μ2 > 0
Calculate the test statistic and P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.)
t=
P-value=
State the conclusion in the problem context.
a) Reject H0. The data suggests that the true mean HAZ depth is larger when the current setting is higher.
b) Fail to reject H0. The data does not suggest that the true mean HAZ depth is larger when the current setting is higher.
c) Fail to reject H0. The data suggests that the true mean HAZ depth is larger when the current setting is higher.
d) Reject H0. The data does not suggest that the true mean HAZ depth is larger when the current setting is higher.