Answered: Independent random samples from regions…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

Independent random samples from regions in Tara gave the following phosphorous measurements (in ppm).
Assume the population distributions of phosphorous are mound-shaped and symmetric for this region.
Region: ?; ? = 12
580 810 790 790 340 800 890 860 840 640 970 720

d. Find a 90% confidence interval for ?.
e. Interpret your result in (d).

Expert Solution

Step 1

Given

data set: 580,810,790,790,340,800,890,860,840,640,970,720

n=12

$C o n f i d e n c e i n t e r v a l = 90 % α = s i g n i f i c a n c e l e v e l = 1 - 0.90 = 0.10$

$\bar{x} = m e a n o f s a m p l e d a t a = 752.5 s = s a m p l e s \tan d a r d d e v i a t i o n = 167.1757 (b y u \sin g E x c e l)$

Step 2

$d) T h e C o n f i d e n c e I n t e r v a l f o r p o p u l a t i o n m e a n μ i s : \bar{x} - t_{\frac{α}{2}, d f} \times \frac{s}{\sqrt{n}} < μ < \bar{x} + t_{\frac{α}{2}, d f} \times \frac{s}{\sqrt{n}} D e g r e e o f f r e e d o m : d f = n - 1 = 12 - 1 = 11 T h e c r i t i c a l v a l u e : t_{\frac{0.10}{2}, 11} = 1.796$

$T h e m a r g i n o f e r r o r i s : E = t_{\frac{α}{2}, d f} \times \frac{s}{\sqrt{n}} = 1.796 \times \frac{167.1757}{\sqrt{12}} = 86.674$

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