Answered: A bag contains 10 marbles, each marble…

Name: A bag contains 10 marbles, each marble is either red or blue. You clai
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Description: A bag contains 10 marbles, each marble is either red or blue. You claim that four of them are red. To test this claim you take out 5 marbles from the bag and find that 1 of them is red. Test the claim. Determine the p-value and write the answer round

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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A bag contains 10 marbles, each marble is either red or blue. You claim that four of them are red. To test this claim you take out 5 marbles from the bag and find that 1 of them is red. Test the claim. Determine the p-value and write the answer rounded to four decimal places.

Expert Solution

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Let p be the number of red marbles in the bag full of 10 marbles. My claim is there are 4 marbles in the bag.

$P r o b a b i l i t y o f g e t t i n g a r e d m a r b l e = \frac{4}{10} = 0.4 W e c o n s i d e r t h e f o l l o w i n g h y p o t h e s i s : - H_{0} : p = 0.4 v e r s u s H_{1} : p \neq 0.4 L e t X_{i} = \{\begin{cases} 1, i f t h e m a r b l e i s r e d \\ 0, o t h e r w i s e \end{cases} U n d e r H_{0}, X = \sum_{i = 1}^{n} X_{i} ~ b i n (5, 0.4) L e t x_{0} b e t h e o b s e r v e d v a l u e o f X w h i c h i s 1 i n t h i s c a s e . T h e n, p - v a l u e = 2 \times m i n {P_{H_{0}} [X \geq 1 | p = 0.4], P_{H_{0}} [X \leq 1 | p = 0.4]}$

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