Type II error occurs when:

Correct option is C

Introduction:

A Type II error occurs when the null hypothesis (H₀) is false but is accepted (i.e., not rejected). In simple terms, we fail to detect an effect or difference when one actually exists. This is also called a false negative.

In hypothesis testing, when we make a decision about the null hypothesis, there are four possible outcomes:

• If H₀ is true and we accept it → Correct decision

• If H₀ is true and we reject it → Type I error (false positive)

• If H₀ is false and we reject it → Correct decision

• If H₀ is false and we accept it → Type II error (false negative)

So, when we accept a false null hypothesis, we commit a Type II error.

Information Booster:

• Type II error (β) means we fail to reject a false null hypothesis.

• It leads to missing a real effect, such as failing to detect the success of a treatment.

• The probability of making a Type II error is denoted by β, and the power of a test is defined as 1 − β.

• A powerful test has a low probability of Type II error.

• Type II error can be minimized by increasing the sample size or using more sensitive testing methods.

• In fields like medicine or manufacturing, Type II errors can lead to risky decisions due to missed detections.

• Statisticians carefully design studies to balance both Type I and Type II error risks.

  Additional Information :

• Option (a): H₀ is true and is accepted .This is a correct decision, not an error. If the null hypothesis is actually true and we accept it, there’s no mistake.
  

• Option (b): H₀ is true and is rejected
  This is a Type I error. Here, we reject a true null hypothesis — a false positive — thinking an effect exists when it doesn’t.

• Option (d): Hₐ is false and is rejected
  This is again a correct decision. If the alternative hypothesis is false and we reject it, then our conclusion is accurate.

  True Situation	Decision: Accept H₀	Decision: Reject H₀
  H₀ True	Correct (1-α)	Type I Error (α)
  H₀ False	Type II Error (β)	Correct (Power = 1-β)