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
- 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
- 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
- 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
- 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