Calculate the Type I and Type 2 Error Rates Example (1): Consider a fire-alarm w

Question

Calculate the Type I and Type 2 Error Rates

Example (1): Consider a fire-alarm which is being produced. It is important to differentiate the random process and the population. In this case, both are quite easy to describe. The population has only two elements: there is a fire, there is not a fire}. The random process is listening to the alarm, there also only two outcomes here: fthe fire alarm makes noise, the fire alarm is silent^. The process of listening to the fire-alarm (or identically, observing what state the alarm is in: either sounding or silent) has only two states and so this is a Bernoulli random variable. In a perfect world, the fire alarm would only go off when there is a fire. However, we do not live in a perfect world, and false alarms do exist (although we attempt to minimize them). We can then consider a rigorus set of lab and real-world tests of these particular fire-alarms, and we tabulate the results below: Fire Alarm Silent Fire Alarm Sounds 97 There is a Fire There is no Fire 94 Suppose we choose the null hypothesis to be the case where there is a fire and we choose the alternate hypothesis to be the case where there is not a fire. Then we can re-lable the above table as Reject Ho Accept Ho 97 Ho is True Ho is False 94 Calculate the Type-I and Type-II error rates

Explanation / Answer

In statistical hypothesis testing, a type I error is the incorrect rejection of a true null hypothesis (a "false positive"), while a type II error is incorrectly retaining a false null hypothesis (a "false negative").

type i error = 3/(100)=0.03

type ii error =6/100 =0.06

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