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Consider the situation of Example 1.1 in Chapter 1 in the notes (involving the h

ID: 3226528 • Letter: C

Question

Consider the situation of Example 1.1 in Chapter 1 in the notes (involving the heat treatment of gears).

b) Make and interpret 90% two-sided and one-sided confidence intervals for the improvement in mean runout produced by the laying method over the hanging method (for the one-sided interval, give a lower bound for mu_hung - mu_laid). c) Make and interpret a 90% two-sided confidence interval for the mean runout for laid gears. A process engineer is faced with the question, 'How should gears be loaded into a continuous carburizing furnace in order to minimize distortion during heat treating?' The engineer conducts a well-thought-out study and obtains the runout values for 38 gears laid and 39 gears hung.

Explanation / Answer

b)

Two-Sample T-Test and CI: hung, laid

Two-sample T for hung vs laid

N Mean StDev SE Mean
hung 39 17.95 6.92 1.1
laid 37 12.65 3.90 0.64


Difference = mu (hung) - mu (laid)
Estimate for difference: 5.30
90% lower bound for difference: (3.62,INF) this is the lower 90% confidence interval
T-Test of difference = 0 (vs >): T-Value = 4.08 P-Value = 0.000 DF = 74
Both use Pooled StDev = 5.6572

c)

Two-Sample T-Test and CI: hung, laid

Two-sample T for hung vs laid

N Mean StDev SE Mean
hung 39 17.95 6.92 1.1
laid 37 12.65 3.90 0.64


Difference = mu (hung) - mu (laid)
Estimate for difference: 5.30
90% CI for difference: (3.14, 7.46)this is the both sided 90% confidence interval
T-Test of difference = 0 (vs not =): T-Value = 4.08 P-Value = 0.000 DF = 74
Both use Pooled StDev = 5.6572