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An investigator commits type II error when he/she

An investigator commits type II error when he/she Correct Answer accepts a null hypothesis when it is false

Errors In Hypothesis Testing

Type-I error corresponds to rejecting H0 (Null hypothesis) when H0 is actually true, and a Type-II error corresponds to accepting H0 (Null hypothesis)when H0 is false. Hence four possibilities may arise.

  1. The null hypothesis is true but the test rejects it (Type-I error).
  2. The null hypothesis is false but the test accepts it (Type-II error).
  3. The null hypothesis is true and the test accepts it (correct decision).
  4. The null hypothesis is false and test rejects it (correct decision)

1) Type-I Error:

  • In a hypothesis test, a Type-I error occurs when the null hypothesis is rejected when it is in fact true. That is, H0 is wrongly rejected. For example, in a clinical trial of a new drug, the null hypothesis might be that the new drug is no better, on average than the current drug. That is, there is no difference between the two drugs on average.
  • A Type-I error would occur if we concluded that the two drugs produced different effects when in fact there was no difference between them. A Type-I error is often considered to be more serious, and therefore more important to avoid than a Type-II error.
  • The exact probability of a Type-I error is generally unknown. If we do not reject the null hypothesis, it may still be false (a Type-I error) as the sample may not be big enough to identify the falseness of the null hypothesis (especially if the truth is very close to the hypothesis).

Important Points

2) Type-II Error

  • In a hypothesis test, a Type-II error occurs when the null hypothesis, H0, is not rejected when it is in fact false.
  • For example, in a clinical trial of a new drug, the null hypothesis might be that the new drug is no better, on average than the current drug; that is Ho: there is no difference between the two drugs on average.
  • A Type-II error would occur if it was concluded that the two drugs produced the same effect, that is, there is no difference between the two drugs on average, when in fact they produced different effects.
  • A Type-II error is frequently due to sample sizes being too small.
  • The probability of a Type-II error is symbolized by â and written: P (Type-II error) = â (but is generally unknown).
  • A Type-II error can also be referred to as an error of the second kind.

​Hence, An investigator commits type II error when he/she accepts a null hypothesis when it is false.

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