Evaluation Of Decision Error

Four possible outcomes that determine whether a decision is correct or an error:

It is not possible to simultaneously commit a Type I(α) error and Type II (β)decision error.
In short, either an alpha (α) or beta (β) decision error can be made, but not both.

Probability of rejecting the null hypothesis when it is true is called type I error, designated by Greek letter α Alpha.
Example
- A toy manufacturing company set a limit of 2% defective from the woodenparts it receives from its vendor.
- A sample of 500 parts out of 4000 lot size received revealed that 11 parts were defective, translating to 2.2% greater than 2%.
- The customer rejectedthe Shipment.
- A 100% inspection from the vendor revealed that only 50 parts were defective out of 4000 parts, i.e., 1.25% defective.
- In this case, only 1.25% of the parts were defective against an acceptable level of 2% defective, and rejecting the shipment was an error.
- In terms of hypothesis testing language, we say that we rejected the Null Hypothesis, but the shipment wasnot substandard.
- We committed a Type 1 Error.

Probability of committing another type of error , called a type II error, designated by Greek letter β ,beta
Type II error – Accepting the null hypothesis when it is actually false
Example
- In the example, the toy manufacturer would commit a type II error if a shipment from a supplier containing greater than 2% defective, yetthe shipment was accepted.
- How could this happen?
- Suppose 9 out of the 500 parts in the sample tested were substandard, leading to 1.8% defective. As per the guideline, the sample contained less than 2% defective and hence was accepted.
- What if, by chance, the 90 defective parts out of 4000 lots leading to 2.25% defective greater than 2%
- Since the person doing analysis cannot study every item in the population, thus there is the possibility of two types of errors, Alpha error α, and beta errorβ