Question

One of the occupational hazards of being an airplane pilot is the hearing loss that results from being exposed to high noise levels. To document the magnitude of the problem, a team of re- searchers measured the cockpit noise levels in 18 commercial aircraft. The results (in decibels) are as follows (84). Plane Noise Level (dB) Plane Noise Level (dB) (a) Assume that cockpit noise levels are normally distributed. Use Theorem 7.3.4 to construct a 95% confidence interval for the standard deviation of noise levels from plane to plane. (b) Use these same data to construct two one-sided 95% confidence intervals for o.

Answer 1

Ulven the data ; Lett be the noise level (DE). Noise level (dB)(0) ( -2) I Gel- og -6.39 -3.39 oc -0-39 1.6! 1.61 4.61 -0-39 -5.39 - 5:39 40.8321 11.4921 0.152) 2.5921 2.5921 216 2521 0.1521 29.0521 29.0521 70.3921 9203521 43,6921 54-6121 608121 31.4721 6-8121 6.8121 -8.39 9.61 6.61 -7.39 2.61 5.61 2-61 2061 -0.39 0.1521 1447 450.2778 3- SE 1447 = 30-3889. = 80-39. gla js(x2-x)* = (450- 2778) = 25.0154 Noise levels are Normally destitulich. we cose Xº dist to construct confidence Interval

95% confidence Decalien (n-1) 5² X(n-1) / Interval ber Standard standard col -)s" J x(n-1) * 1/2 ne 18, S 25.0154. XE8-1) 0-05 = x*(17) 0-095 = 30-191 X=(18-1) 1-0-095 = X 17 0.975 = 4-56ce. © (n-1)3 va Ens) a12 - Soal 6-1) 52 v Kön-1) (1-4) (17) (25.0152sos (11) (25.01su) 300191 9.564 425.2618 425.2618 - Sos 30-191 4.564 so? 15602218 1886 ✓ ru 08571429 304530939625095 704981 | 3-153) LOE 7.4981