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(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鈥H0:=6.7versusHa:<6.7 or the one from part (a) of this exercise鈥攚ould you be

more interested in? Justify your answer.

Short Answer

Expert verified

a. H0:p=0.78for null hypothesis and H0:p>0.78for alternative hypothesis

b. Type I error - the training needs improvement and Type II error - training needs no improvement

c. Type I error is more serious in this setting

d. With the population proportion of0.78

Step by step solution

01

introduction

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

02

explanation part (a)

Given,

population proportion is 78%or 0.78

Calculating the null and alternative hypotheses,

H0:p=0.78as per the null hypothesis and H0:p>0.78ass per the alternative hypothesis

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

03

explanation part (b)

In Type I error population proportion is 0.78that 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 than0.78for the responder that showed up 8minutes 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.

04

explanation part (c)

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.

05

explanation part (d)

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

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