When is a Type II error more likely?

When is a Type II error more likely?

• A. small sample size
• B. alpha is high
• C. power is high
• D. the sample size is large

Answer: (A)

Type II error happens when you fail to reject a null hypothesis that is actually false. This risk rises when study power is low. Power is the probability of detecting a true effect, and it gets weaker as sampling variability increases. A small sample size increases variability and makes it harder for the test statistic to cross the boundary needed to declare a difference, so you’re more likely to miss a real effect. In contrast, higher alpha makes it easier to reject the null, boosting power and reducing the chance of a Type II error; a larger sample size also raises power and lowers this risk. So the scenario most likely to yield a Type II error is a small sample size.

Type II error happens when you fail to reject a null hypothesis that is actually false. This risk rises when study power is low. Power is the probability of detecting a true effect, and it gets weaker as sampling variability increases. A small sample size increases variability and makes it harder for the test statistic to cross the boundary needed to declare a difference, so you’re more likely to miss a real effect.

In contrast, higher alpha makes it easier to reject the null, boosting power and reducing the chance of a Type II error; a larger sample size also raises power and lowers this risk. So the scenario most likely to yield a Type II error is a small sample size.