Question

A test of  H₀: μ = 20 versus H₁: μ > 20  is performed using a significance level of α = 0.05. The value of the test statistic is z = 1.47.

If the true value of μ is 25, does the test conclusion result in a Type I error, a Type II error, or a Correct decision?

Answer 1

Type 1 error is rejecting the true null hypothesis

Type 2 error is failing to reject the false null hypothesis

Now P value is P(z>1.47)=0.0708

Here P value is greater than alpha=0.05, so we fail to reject the null hypothesis

Now here μ is 25, hence we made Type 2 error