Question

Explain Type I and Type II errors in detail ( with example of your choice). Define level of significance and p Values. Interpret P-value of 0.023 in Hypothesis testing in general.

Answer 1

Ans:

Type I error

When the null hypothesis is true and you reject it, you make a type I error. The probability of making a type I error is α, which is the level of significance you set for your hypothesis test. An α of 0.05 indicates that you are willing to accept a 5% chance that you are wrong when you reject the null hypothesis. To lower this risk, you must use a lower value for α. However, using a lower value for alpha means that you will be less likely to detect a true difference if one really exists.

Type II error

When the null hypothesis is false and you fail to reject it, you make a type II error. The probability of making a type II error is β, which depends on the power of the test. You can decrease your risk of committing a type II error by ensuring your test has enough power. You can do this by ensuring your sample size is large enough to detect a practical difference when one truly exists.

Example:

A medical researcher wants to compare the effectiveness of two medications. The null and alternative hypotheses are:

• Null hypothesis (H₀): μ₁= μ₂

  The two medications are equally effective.

• Alternative hypothesis (H₁): μ₁≠ μ₂

  The two medications are not equally effective.

A type I error occurs if the researcher rejects the null hypothesis and concludes that the two medications are different when, in fact, they are not. If the medications have the same effectiveness, the researcher may not consider this error too severe because the patients still benefit from the same level of effectiveness regardless of which medicine they take.

However, if a type II error occurs, the researcher fails to reject the null hypothesis when it should be rejected. That is, the researcher concludes that the medications are the same when, in fact, they are different. This error is potentially life-threatening if the less-effective medication is sold to the public instead of the more effective one.

The P value, or calculated probability, is the probability of finding the observed, or more extreme, results when the null hypothesis (H ₀) of a study question is true – the definition of 'extreme' depends on how the hypothesis is being tested.

The level of significance is defined as the probability of rejecting a null hypothesis by the test when it is really true, which is denoted as α. That is, P (Type I error) = α.

Suppose,level of significance,alpha=0.05

if p-value=0.023

As,p-value<0.05,we reject the null hypothesis.