(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.

(d) If you sustain a life-threatening injury due to a vehicle accident, you want to receive medical treatment as quickly as possible. Which of the two significance tests—$H_0:\mu =6.7\text{versus}{H}_a:\mu <6.7$ or the one from part (a) of this exercise—would you be

more interested in? Justify your answer.

The null hypothesis is a general explanation that expresses that there is no relationship between two peculiarities viable or that there is no relationship between two gatherings. An alternative hypothesis is an explanation that portrays that there is a relationship between two selected variables in a review

Given,

population proportion is $78\%$or $0.78$

Calculating the null and alternative hypotheses,

$H_0:p=0.78$as per the null hypothesis and $H_0:p>0.78$ass per the alternative hypothesis

Thus, the population proportion is equal to $0.78$for null hypothesis and greater than $0.78$ for the alternative hypothesis.

In Type I error population proportion is $0.78$that the first responder showed up quite a while after the mishap, yet it demonstrates that it is more. The result is that the reaction time has improved and the preparation doesn't need to be improved, however actually the preparation needs to move along.

In Type II error, when the null hypothesis is valid then dismissal of null hypothesis also failed. The population proportion is greater than$0.78$for the responder that showed up $8$minutes after the mishap. Subsequently, rather than the reaction time, training should be improving, yet in reality, the preparation should not be gotten to the next level.

In Type II error The training has improved yet in Type I error, the training is not improved however in reality preparing should be worked on in Type I error.

Hence, Type I error is more serious.

The one with the population proportion $0.78$since the significance test population mean is not more than $6.7$minutes.