Answered: A company gives the percentage of…

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015

1st Edition

ISBN:9781680331141

Author:HOUGHTON MIFFLIN HARCOURT

Publisher:HOUGHTON MIFFLIN HARCOURT

Chapter11: Data Analysis And Displays

Section: Chapter Questions

Problem 2CR

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Question

A company gives the percentage of defective products as 6% or less. Use the sample below to calculate the test statistics that would be used to determine if this has increased. Round 2 decimal places. Sample size = 50 Number defective = 5

Expert Solution

Step 1

Given:

$p_{0} = 0.06 n = 50 x = 5$

The significance level is taken as 0.05.

Step 2

$\begin{array}{rcl} \hat{p} & = & \frac{x}{n} \\ = & \frac{5}{50} \\ = & 0.1 \end{array}$

Hypothesis:

$H 0 : p \leq 0.6$

H0:The percentage of defective is less than or equal to 6%.

H1:p>0.6

H1: The percentage of defective is greater than 6%.

Test statistic

$\begin{array}{rcl} z & = & \frac{\hat{p} - p_{0}}{\sqrt{\frac{p_{0} (1 - p_{0})}{n}}} \\ = & \frac{0.1 - 0.06}{\sqrt{\frac{0.06 (1 - 0.06)}{50}}} \\ = & 1.191 \end{array}$

Test statistic =1.19

using the excel formula "=1-NORM.S.DIST(1.19,TRUE)" p-value =0.117

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