Question

When a process goes out of control, failing to detect the change leads to a type II error. Several factors affect the type II error probability such as sample size (n), type I error probability (α), the magnitude of shift (∣δ∣). To control type II error probability, select all that applies:

For a fixed α and ∣δ∣, type II error probability decreases with increase in n
For a fixed α and n, type II error probability decreases with increase in ∣δ∣
For a fixed α and ∣δ∣, type Il error probability increases with increase in n
For a fixed α and n, type II error probability icnreases with increase in ∣δ∣ It's all relative

Answer 1

To control the Type II error probability, we want to decrease the probability of making a Type II error. This can be achieved by increasing the sample size (n) and increasing the magnitude of shift (∣δ∣) with a fixed α.

Step-by-step explanation:

The probability of making a Type II error increases with an increase in sample size (n), for a fixed α and ∣δ∣.

Similarly, the probability of making a Type II error increases with an increase in the magnitude of shift (∣δ∣), for a fixed α and n.

To control the Type II error probability, we want to decrease the probability of making a Type II error. This can be achieved by increasing the sample size (n) and increasing the magnitude of shift (∣δ∣) with a fixed α.