Exercises 21 and 22 refer to the following setting. 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 mu =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. 22. 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.

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Exercises 21 and 22 refer to the following setting. 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 mu =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. 22. 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.

Answer 1

(a) The parameter of interest is the proportion of calls on which emergency personnel arrive within 8 minutes. The null hypothesis is that the proportion is equal to 78%, while the alternative hypothesis is that the proportion is greater than 78%.<br /><br />(b) A Type I error would be rejecting the null hypothesis when it is true, which would mean concluding that first responders are arriving within 8 minutes more often than 78% of the time when in fact they are not. This could lead to unnecessary changes or interventions to improve response times. A Type II error would be failing to reject the null hypothesis when it is false, which would mean concluding that first responders are not arriving within 8 minutes more often than 78% of the time when in fact they are. This could lead to a failure to identify an opportunity to improve response times.<br /><br />(c) In this setting, a Type II error is more serious because it would mean that there is a failure to identify an opportunity to improve response times, which could have serious consequences for accident victims.

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