Question: 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, the mean response time to all accidents involving life-threatening injuries last year was m = 6.7 minutes. Emergency personnel arrived within 8 minutes on 78% of all calls involving life-threatening injuries last year. The city manager shares this information and encourages these first responders to "do better." At the end of the year, the city manager selects an SRS of 400 calls involving life-threatening injuries and examines the response times.
Awful accidents
(a) State hypotheses for a significance test to determine whether first responders are arriving within 8 minutes of the call more often. Be sure to define the parameter of interest.
(b) Describe a Type I error and a Type II error in this setting and explain the consequences of each.
(c) Which is more serious in this setting: a Type I error or a Type II error? Justify your answer.