The Ledd Pipe Company has received a large shipment of pipes, and a quality cont
ID: 3153360 • Letter: T
Question
The Ledd Pipe Company has received a large shipment of pipes, and a quality control inspector wants to estimate the average diameter of the pipes to see if they meet minimum standards. In particular, the average diameter of the pipes must not differ significantly from 2.52 mm. She takes a random sample of 15 pipes, and the sample produces an average diameter of 2.55 mm with a standard deviation of 0.07 mm. Assume that the diameters of the pipes are normally distributed. Is there enough evidence to conclude that the true average diameter differs from this amount? Use a 1% level of significance.
Explanation / Answer
Formulating the null and alternative hypotheses,
Ho: u = 2.52
Ha: u =/ 2.52
As we can see, this is a two tailed test.
Thus, getting the critical t,
df = n - 1 = 14
tcrit = +/- 2.976842734
Getting the test statistic, as
X = sample mean = 2.55
uo = hypothesized mean = 2.52
n = sample size = 15
s = standard deviation = 0.07
Thus, t = (X - uo) * sqrt(n) / s = 1.659850006
Also, the p value is
p = 0.119168722
As |t| < 2.977, and P > 0.01, we FAIL TO REJECT THE NULL HYPOTHESIS.
Hence, there is no significant evidence that the average diameter of the pipes differ significantly from 2.52 mm. [CONCLUSION]
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