6. Statistical Inference

Errors Power — Quiz

Test your understanding of errors power with 5 practice questions.

Practice Questions

Question 1

A researcher conducts a study to determine if a new fertilizer increases crop yield. The null hypothesis ($H_0$) is that the fertilizer has no effect. The alternative hypothesis ($H_1$) is that the fertilizer increases crop yield. If the fertilizer actually increases crop yield, but the study fails to detect a statistically significant increase, what is the probability of this specific outcome?

Question 2

In a criminal justice system, the null hypothesis ($H_0$) is that a defendant is innocent, and the alternative hypothesis ($H_1$) is that the defendant is guilty. A Type I error in this context would mean:

Question 3

A pharmaceutical company is testing a new drug for a chronic condition. The null hypothesis ($H_0$) is that the drug has no effect. The alternative hypothesis ($H_1$) is that the drug is effective. If the drug is truly effective, but the study concludes it is not, and the study had a statistical power of $0.70$, what is the probability that the study made a Type II error?

Question 4

Which of the following changes would simultaneously increase statistical power and decrease the probability of a Type I error ($\alpha$)?

Question 5

A researcher is investigating the impact of a new teaching method on student test scores. They hypothesize that the new method will improve scores. They conduct a study and find a p-value of $0.06$. If their chosen significance level ($\alpha$) is $0.05$, what is the appropriate conclusion and potential error?