ESS210B
Prof. Jin-Yi Yu
Example
A
manufacturer of car batteries claims that the life of his batteries is approximately
normally distributed with a standard deviation equal to 0.9
year. If a random sample of 10 of these batteries has a standard deviation
of 1.2 years, do you think that s > 0.9 year? Use a 0.05 level of
significance.
1. Ho:
s2 = 0.81
H1: s2 > 0.81
2.a =
0.05
3.Critical
region: c2 > 16.919, where c2 =(n-1)S2/ s2 with degree of freedom=9
4.From
the sampling: S2=1.44,
n=10,
c2 = (10-1)(1.44)/0.81 = 16.0 <
16.919
5.
Conclusion: Accept Ho and conclude that these is no reason to doubt
that the standard deviation is 0.9 year.