when the null hypothesis is not rejected, it is possible a type i error has occurred. possible a type ii error has occurred. possible either a type i or a type ii error has occurred. not possible a type ii error has occurred.

A null hypothesis being a statistical hypothesis, states that no statistical significance can be present in a set of observations. Usually, hypothesis testing is a method used to judge the veracity of a given sample.

Sometimes, it is called just null, or even it has a symbol, viz, [tex]H_0[/tex].

We consider generally 4 cases:

[tex]H_0[/tex] is accepted when [tex]H_0[/tex] is true ⇒ A correct decision
[tex]H_0[/tex] is rejected but is true⇒ Type i error has occurred and is rejected by us, null hypothesis is present
[tex]H_0[/tex] is false but is accepted by us⇒ Type ii error has occurred, null hypothesis is not present.
[tex]H_0[/tex] is false and is rejected⇒ A correct decision.

According to the given question, we have not rejected the null hypothesis.

Thus, we have two options present, either the type ii error has occurred and null hypothesis is not present, or the null hypothesis is present.

Concluding, when a null hypothesis is accepted, it is possible that a type ii error has occurred.

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