Question

The Ledd Pipe Company has received a large shipment of pipes, and a quality control inspector wishes to
estimate the average diameter of these pipes. A random sample of 18 pipes produces an average diameter of
2.56 mm with a standard deviation of 0.05 mm.
The average diameter of the pipes must not differ significantly from 2.52 mm. Is there enough evidence at
the 5% level of significance to conclude that the true average diameter differs from this amount? Conduct an
appropriate hypothesis test using (i) the p-value method, (ii) the rejection point method, and (iii) the confidence
interval method.

Answer 1

n = 18
xbar = 2.56 s = 0.05
H0 : mu = 2.52 H1: mu not equal 2.52

test stat = t = (xbar-mu)/(s/sqrt(n)) = 3.39
p-value = 0.003 < 0.05 Reject H0
t-critical = 2.11 < 3.39 Reject H0

CI =(xbar-t-critical*s/sqrt(n), xbar+t-critical*s/sqrt(n))
(2.54, 2.58)