Question

The standard deviation for parts from two machines are known to be .03 mm. Machine A produced a random sample of 40 parts with a mean size of 16.8 mm. Machine B produced a random sample of 42 parts with a mean size of 17.0 mm. Does this show, at 90% confidence, that the machines have different average sizes? Be sure to state the interval.

		I am 90% confident that the difference in the average sizes of parts from the two machines is between -.2109 and -.1891. We failed to show a difference.
		I am 90% confident that the difference in the average sizes of parts from the twomachines is between -.2109 and -.1891. The evidence suggests the averages are different.
		I am 90% confident that the difference in the average sizes of parts from the twomachines is between -.4155 and -.1021. We failed to show a difference.
		I am 90% confident that the difference in the average sizes of parts from the twomachines is between -.4155 and -.1021. The evidence suggests the averages are different.

Answer 1

	Machine A		Machine B
x1            =	16.80	x2            =	17.00
n1           =	40	n2           =	42
σ1           =	0.03	σ2           =	0.03
std error σx1-x2=√(σ21/n1+σ22/n2)    =	0.0066

Point estimate of differnce '=x1-x2 =	-0.200
for 90 % CI value of z=		1.645
margin of error E=z*std error =	0.011
lower bound=(x1-x2)-E =	-0.2109
Upper bound=(x1-x2)+E =	-0.1891

I am 90% confident that the difference in the average sizes of parts from the twomachines is between -.2109 and -.1891. The evidence suggests the averages are different.

(since interval values does not contain 0)