Answer:
a)
b) The Type I error occurs when we reject a null hypothesis that is actually true. In this case, it means we conclude that the arrival time have improved, when it didn't.
The Type II error occurs when we accept a null hypothesis that is actually false. In this case, although the arrival times have really improved, the evidence from the sample was not enough to show that improvement.
c) In this case, the Type I error is more serious, because it gives the wrong impression of improvement and no further actions will be taken to reduce the times.
Step-by-step explanation:
a) If you want to determine if the responders are arriving within 8 minutes of the call more often, you have to evaluate the proportion of accidents in which the arrival time is less than 8 minutes and compare it with the known proportion of π=0.78.
The sample parameter "p: proportion of accidents with arrival time of 8 minutes or less" will be used to test the hypothesis.
The null and alternative hypothesis will be: