Answered: Let p denote the population proportion…

Name: Let p denote the population proportion of (budget) LCD panels that hav
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Description: Let p denote the population proportion of (budget) LCD panels that have defective pixels. A researcher randomly selected 100 panels and determined that 8 have defective pixels. She wants to test H0 : p = 0.15 versus Ha : p < 0.15 at the α = 0.01 sign

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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Let p denote the population proportion of (budget) LCD panels that have defective pixels. A researcher randomly selected 100 panels and determined that 8 have defective pixels. She wants to test H0 : p = 0.15 versus Ha : p < 0.15 at the α = 0.01 significance level (using the score test). Which of the following is/are true? (A) H0 is rejected (B) We have evidence that p = 0.15 (C) p−value = 0.050 (D) p−value = 0.025

Answer Choices:

None of the other answers are correct

(B) only

(B) and (C)

(A) only

(B) and (D)

Expert Solution

Step 1

Given that,

Sample size $n = 100$

Sample proportion of panels that have defective pixels $\hat{p} = \frac{8}{100} = 0.08$

Step 2

Hypothesis:

$H_{0} : p = 0.15$

$H_{a} : p < 0.15$

Test statistic:

$\begin{array}{rcl} z & = & \frac{\hat{p} - p}{\sqrt{\frac{p (1 - p)}{n}}} \\ = & \frac{0.08 - 0.15}{\sqrt{\frac{0.15 (1 - 0.15)}{100}}} \\ = & - 1.96 \end{array}$

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