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Unformatted text preview: Fall 2009 Hansen
Assignment 11 solutions
Due 11/24/2009 9:10 AM 1. Problem 7.9 in Ross.
~ 0, , = 0.08,
a) − 1.96 , + 1.96 b) −∞, + 1.645
− 1.645 c) = 10, = 11.48 = 11.48 − 1.96 , ∞ = 11.44, ∞ Confidence interval for : − ,+ , = 24, = 333.996, b) . = 11.43, 11.53 = 0,11.52 PCB concentration in fish can’t be less than zero. 2. Problem 7.17 in Ross.
unknown; use tdistribution a) , 11.48 + 1.96 . = = 0.05, . , = 2.069
2sided 95% CI: 331.06, 336.93 , 1
−1 − = 6.9576 = 0.01, . , = 2.807
2sided 99% CI: 330, 338 3. Problem 7.20 in Ross.
= 16, = 2200, = 800
We want 2sided 90% CI for 2200 − 1.753 ∗ , = . , = 1.753 800
800
, 2200 + 1.753 ∗
= 1849.4, 2550.6
4
4 4. Problem 7.41 in Ross.
= = 10
= 3358.1, = 3130.4
= 352.7311, = 133.1492
= = 0.10 = 71073.955 Fall 2009 Hansen a) 2sided 95% confidence interval
= 0.05, . , = 2.101
− ± ∗ , b) Upper 1sided 95% confidence interval
= 1.734
.,
20.96, ∞
c) Lower 1sided 95% confidence interval
−∞, 434.44 1 + 1 = −22.8,478.19 5. Problem 7.50 in Ross.
Formula from Ross, page 266: 1− = We know that we must collect at least samples according to the formula above.
However, before we start collecting samples we have no idea what is going to be.
Therefore, what we can do is simply make sure that we collect as large as is necessary,
which it will be if 1 − is as large as possible.
If
= 1−
Find = 1 − 2 = 0 such that = 0.5 (where 0 ≤ And then the largest sample we need to collect will be
From the question we know = 0.10
= 1.645 and = 0.02 ∗ 2
.
And = 1.645
= 1691
0.04 ≤1 = ∗= ...
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 Fall '10
 hansen

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