91Ó°ÊÓ

Clean water The Environmental Protection Agency (EPA) has determined that safe

drinking water should contain at most $1.3$mg/liter of copper, on average. A water supply company is testing water from a new source and collects water in small bottles at each of$30$randomly selected locations. The company performs a test at the α=0.05 significance level of$H_0:\mathrm{μ}=1.3$versus $H_a:\mathrm{μ}>1.3$, where μ is the

true mean copper content of the water from the new source.

a. Describe a Type I error and a Type II error in this setting.

b. Which type of error is more serious in this case? Justify your answer.

c. Based on your answer to part (b), do you agree with the company’s choice of $\mathrm{Î\pm }=0.05$? Why or why not?

Step by step solution

01

Given Information

It is given that $H_0:\mathrm{μ}=1.3$

$H_1:\mathrm{μ}>1.3$

02

Explaining type I and type II error

Type I error: There is enough convincing evidence that true mean copper content from new source is $1.3$mg/l, when actual mean content of water from new source is $1.3$mg/l.

Type II error: Noconvincing evidence is present true mean copper content from new source is $1.3$mg/l when actual mean content of water from new source is over$1.3$ mg/l

03

Which error is worse

Here, type II error is worse as when water is not safe, people might drink it.

04

Choice of α

As type II error is more worse.

The chances of type II error decreases with increase in type I error and $\mathrm{Î\pm }$would be better.

Hence, $\mathrm{Î\pm }=0.10$is preferred over$0.05$

Unlock Step-by-Step Solutions & Ace Your Exams!

• Full Textbook Solutions

  Get detailed explanations and key concepts

• Unlimited Al creation

  Al flashcards, explanations, exams and more...

• Ads-free access

  To over 500 millions flashcards

• Money-back guarantee

  We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!