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 “do better.” 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 α = 0.05 level of H₀: 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’s choice of α = 0.05? Why or why not?