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1. Arandomsample of size n = 19 is drnwn from a normal distribution for which a2 = 12.0. In what range are we likely to find the sample variance, s2? Answer the question by finding two numbers a and b such that
P(a s s2
b) = 0.95
2. One of the occupational hazards of being an airplane pilot is I.he hearing loss that results from being exposed to high noise levels. To document the magnitude of the problem, a team of researchers measured the cockpit noise levels in 18 commercial aircraft. The results (in decibels) are as follows (94).
Plane
1
Noise Level
74
10
72
2
77
11
90
3
80
12
87
4
82
13
73
5
14
83
6
85
15
86
7
16
8
75
17
9
18
(ii) Assume that cockpit noise levels are normally distributed. Use Theorem 7.5.1 to construct a 95% confidence interval for the standard deviation of noise levels ftom plane to plane.
(b) Use these same data lo construct two one-sided 95% confidence intervals for a.
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