Q 25. Awful accidents Slow response ti... [FREE SOLUTION]

91影视

The Practice of Statistics for AP Examination

Daren Starnes, Josh Tabor

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 837 pages

ISBN: 9781319113339

Chapter 9: Q 25. (page 565)

Awful accidents Slow response times by paramedics, firefighters, and policemen can have serious consequences for accident victims. In the case of life-threatening injuries, victims generally need medical attention within $8$ minutes of the accident. Several cities have begun to monitor emergency response times. In one such city, emergency personnel took more than $8$ minutes to arrive on $22 %$ of all calls involving life-threatening injuries last year. The city manager shares this information and encourages these first responders to 鈥渄o better.鈥� After $6$ months, the city manager selects an SRS of 400 calls involving life- threatening injuries and examines the response times. She then performs a test at the $伪 = 0.05$ level of $H_{0}$ : $p = 0.22$ versus $H_{a} : p < 0.22$ , where $p$ is the true proportion of calls involving life-threatening injuries during this $6$ -month period for which emergency personnel took more than $8$ minutes to arrive.
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 manager鈥檚 choice of $伪 = 0.05$ ? Why or why not?

Short Answer

Expert verified

a. Type I error is rejecting null hypothesis $H_{0}$ , once $H_{0}$ is true and Type II error fail to reject null hypothesis when $H_{0}$ is false.

b. In this case, type II error is more serious.

c. It is better to use $伪 = 0.05$ .

Step by step solution

Given Information

It is given that $H_{0} : p = 0.22$

$H_{1} : p < 0.22$

Explaining type I and type II error

Type I error:Enough convincing evidence is present that correct proportion of calls involves life threatening injuries in case personnel takes more than $8$ minutes to arrive is $< 0.22$ when correct proportion of calls involves life threatening injuries in case personnel takes more than $8$ minutes to arrive is actually $0.22$

Type II error: No convincing evidence is present that correct proportion of calls involves life threatening injuries in case personnel takes more than $8$ minutes to arrive is less than $0.22$ when correct proportion of calls involves life threatening injuries in case personnel takes more than $8$ minutes to arrive is actually over $0.22$