Question

You set up a two-sided hypothesis test for a population mean μ with a null hypothesis of H0:μ=100. You chose a significance level of α=0.05. The p-value calculated from the data is 0.12, and hence you failed to reject the null hypothesis. Suppose that after your analysis was completed and published, an expert informed you that the true value of μ is 104. How would you describe the result of your analysis?

A) A Type 1 error was made because you failed to reject the null hypothesis but μ is really not equal to 100.

B) A Type 2 error was made because you failed to reject the null hypothesis but μ is really not equal to 100.

C) You did not make a Type 1 or Type 2 error.

Answer 1

The correct answer is B) A Type 2 error was made because you failed to reject the null hypothesis but μ is really not equal to 100.

Explanation:

We are testing:

H0:μ = 100

H1:μ ≠ 100 (Since, we are given that a two-sided hypothesis test was used)

Now, our conclusion after the test was conducted was that we failed to reject the null hypothesis, i.e. we did not reject H0. Moreover, we were informed later that the true value of μ is 104, i.e., H1 is true and H0 is not true.

Now, we know that when we fail to reject H0 when in fact H0 is not true, we commit a Type 2 error.

Thus, the correct option is B.

Option A is not correct because we commit a Type 1 error when we reject H0 when in fact H0 is true. This is not the case here.

Option C is not correct because we did commit a Type 2 error.

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