Question

Define a Type I error and a Type II error and explain the consequences of each. A Type I error is:

1) Rejecting a true null hypothesis
2) Failing to reject a false null hypothesis
3) Accepting a true null hypothesis
4) Failing to accept a false null hypothesis

Answer 1

A Type I error occurs when a true null hypothesis is rejected, while a Type II error occurs when a false null hypothesis is not rejected. Consequences of a Type I error include making incorrect conclusions or decisions, while consequences of a Type II error include missing out on important findings or opportunities.

Step-by-step explanation:

A Type I error occurs when a true null hypothesis is rejected, meaning that the decision is to reject the null hypothesis when, in fact, the null hypothesis is true. This error is also known as a false positive. An example of a Type I error is rejecting the null hypothesis that a new drug is ineffective when it actually is effective.

A Type II error occurs when a false null hypothesis is not rejected, meaning that the decision is not to reject the null hypothesis when, in fact, the null hypothesis is false. This error is also known as a false negative. An example of a Type II error is failing to reject the null hypothesis that a new drug is effective when it actually is ineffective.

The consequences of a Type I error can include making incorrect conclusions or decisions based on faulty data. For example, in a legal context, a Type I error could result in convicting an innocent person. The consequences of a Type II error can include missing out on important findings or opportunities. For example, in a medical context, a Type II error could result in failing to detect a serious illness and delaying necessary treatment.