Question

ou conduct a hypothesis test and you observe values for the sample mean and sample standard deviation when n = 25 that do not lead to the rejection of H0 . You calculate a p-value of 0.0667. What is the highest possible significance level you can have?

Answer 1

The higher significance level is 0.0666, as it has to be lower than the p-value.

Significance level is usually expressed up to 2 decimals, so the maximum level of significance is expected to be α=0.06.

Explanation:

We have a hypothesis test for the mean.

The result is that the null hypotesis failed to be rejected.

The P-value is 0.0667.

We have to find the highest possible signficance level.

First, we have to see the decision rule for the p-value method:

1. If the P-value is lower than the significance level, the null hypothesis is rejected.
2. If the P-value is higher than the significance level, the null hypothesis failed to be rejected.

In our question, we are in the second situation, so we can conclude that the P-value is higher than the significance level.

Then, the higher significance level is 0.0666, as it has to be lower than the p-value.

Significance level is usually expressed up to 2 decimals, so the maximum level of significance is expected to be α=0.06.