Through hypothesis testing, it can be explained that Type I error occurs when the allergist determines that the percentage of the population who are allergic to some cheese products is at least 30% when it is actually less than 30%. Similarly, Type II error occurs when the allergist assumes that the percentage of the population who are allergic to certain cheese products is less than 30% when it is actually at least 30%
There are two possible outcomes for hypothesis testing, which leads to two different sorts of conclusion-related errors. This is due to the possibility that the estimated value of the measure and the inference made about the population measure from the samples could diverge.
Let's say an allergist wants to investigate the claim that at least 30% of the population has a cheese allergy.
Let p represent the actual percentage of the population that were allergic to certain cheese products.
The following is how the hypotheses are put forth:
[tex]H_{0}:p < 0.3\\H_{a}:p\geq 0.3[/tex]
The two types of errors that can be committed by the allergist can be described as below:
(a) Type I error:
When the null hypothesis is assumed to be true when it is actually false, type I error arises.
When an allergist determines that the percentage of the population who are allergic to some cheese products is at least 30% when it is actually less than 30%, type I mistake has been committed.
(b) Type II error:
When the null hypothesis is unsuccessfully rejected even when it is false, type II error has occurred.
When an allergist assumes that the percentage of the population who are allergic to certain cheese products is less than 30% when it is actually at least 30%, type II error has occurred.
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