Which one of the following statements is true for Type II error?

Correct option is B

A Type II error occurs when we fail to reject a null hypothesis that is actually false, meaning we are accepting an incorrect hypothesis. This error implies that the test did not detect a difference or effect that actually exists — in other words, a false negative.

In hypothesis testing:

• The null hypothesis (H₀) represents a statement of no effect or no difference.

• The alternative hypothesis (H₁) is what we aim to support (that there is an effect or difference).

A Type II error happens when the test incorrectly concludes that H₀ is true (i.e., "accepted") when in fact, H₀ is false.

Information Booster:

​A Type II error, also known as a false negative, occurs when a statistical test fails to reject a null hypothesis that is actually false. In other words, it mistakenly concludes that there is no effect or difference when one actually exists. This type of error is denoted by β (beta), and the power of a test (1 - β) represents the probability of correctly rejecting a false null hypothesis. The likelihood of committing a Type II error decreases with larger sample sizes, more precise measurements, and stronger effect sizes. In research, committing a Type II error can lead to missed discoveries or the erroneous assumption that an intervention or treatment is ineffective when it truly has an effect.

Additional Knowledge:

(a) Rejecting an incorrect hypothesis
This is actually the correct decision, not an error. Rejecting H₀ when it is false supports the alternative — this is what we ideally aim for in hypothesis testing.

(c) Accepting a correct hypothesis
This is also not an error. If the null hypothesis is correct and we accept it (do not reject), we are making the correct decision.

(d) Rejecting a correct hypothesis
This describes a Type I error, not Type II. In Type I error, we wrongly reject a null hypothesis that is actually true — a false positive.