mayonaisea2ef

2023-02-21

How to calculate Type 1 error and Type 2 error probabilities?

Julien Zavala

Beginner2023-02-22Added 7 answers

Null Hypothesis: $H}_{0}:\mu ={\mu}_{0$

Alternative Hypothesis: $H}_{1}:\mu <,>,\ne {\mu}_{0$

Type 1 errors in hypothesis testing is when you reject the null hypothesis $H}_{0$ but in reality it is true

Type 2 errors in hypothesis testing is when you Accept the null hypothesis $H}_{0$ but in reality it is false

We can think about:

Probability of event $\alpha$ happening, given that $\beta$ has occured:

$P\left(\alpha \mid \beta \right)=\frac{P(\alpha \cap \beta )}{P\left(\beta \right)}$

In light of this, the Type 1 and Type 2 errors in hypothesis testing are as follows:

Type $1$ = $P$( Rejecting $H}_{0$ | $H}_{0$ True)

Type $2$ = $P$( Accept $H}_{0$ | $H}_{0$ False )

Alternative Hypothesis: $H}_{1}:\mu <,>,\ne {\mu}_{0$

Type 1 errors in hypothesis testing is when you reject the null hypothesis $H}_{0$ but in reality it is true

Type 2 errors in hypothesis testing is when you Accept the null hypothesis $H}_{0$ but in reality it is false

We can think about:

Probability of event $\alpha$ happening, given that $\beta$ has occured:

$P\left(\alpha \mid \beta \right)=\frac{P(\alpha \cap \beta )}{P\left(\beta \right)}$

In light of this, the Type 1 and Type 2 errors in hypothesis testing are as follows:

Type $1$ = $P$( Rejecting $H}_{0$ | $H}_{0$ True)

Type $2$ = $P$( Accept $H}_{0$ | $H}_{0$ False )