Question

A random sample of 42 mechanical gears has been collected, and the measurements of
Gear-Diameter (mm) are found below:
130 131 132 130.5 130 130.2 130.7 130 131.2 133
130 130 131 132 133 133 132 131 312.5 131.5
131.2 132.5 130.2 129.5 131 130 130.2 131.5 131.4 131.6
130.6 130.5 131.1 130 13 130 131 130 130 132
131.2 132
(a) Construct a 94% two-bounds confidence interval on the diameter.
(b) Construct a 94% lower confidence bound on the diameter.

Answer 1

(a) 94% two-bounds confidence interval on the diameter: (122.4178 mm, 142.5870 mm)

(b) 94% lower confidence bound on the diameter=124.2239 mm

R code:

x=c(130, 131, 132, 130.5, 130, 130.2, 130.7, 130, 131.2, 133,130, 130, 131,
132, 133, 133, 132, 131, 312.5, 131.5,131.2, 132.5, 130.2, 129.5, 131, 130,
130.2, 131.5, 131.4, 131.6,130.6, 130.5, 131.1, 130, 13, 130, 131, 130, 130, 132,
131.2, 132)
n=length(x)
m=mean(x)
s=sd(x)
#(a)
LL=m-qt(1-0.03,n-1)*s/sqrt(n)
UL=m+qt(1-0.03,n-1)*s/sqrt(n)
round(LL,4)
round(UL,4)
#(b)
LB=m-qt(1-0.06,n-1)*s/sqrt(n)
round(LB,4)