Question

Suppose the national average dollar amount for an automobile insurance claim is $704.05. You work for an agency in Michigan and you are interested in whether or not the state average is less than the national average. The hypotheses for this scenario are as follows: Null Hypothesis: μ ≥ 704.05, Alternative Hypothesis: μ < 704.05. Suppose the true state average is $601.55 and the null hypothesis is not rejected, did a type I, type II, or no error occur?

Answer 1

Given:

The hypotheses for this scenario are as follows:

Null Hypothesis, Ho : μ ≥ 704.05,

Alternative Hypothesis , Ha : μ < 704.05

Type I error :  A type I error occurs when null hypothesis is true but we reject it.

Type II error : Type II error occur when null hypothesis is false but we fail to reject it, means accept the null hypothesis.

Now,

True mean = 601.55

True mean is less than population mean that is null hypothesis is a true. But it is given that null hypothesis is not rejected.

Therefore no error occur.