Type I and Type II Errors

Type I and Type II Errors

Type I Error

Type I error, also known as a “false positive”: the error of rejecting a null hypothesis when it is actually true. In other words, we can say that it is the error of accepting an alternative hypothesis. So the probability of making a type I error in a test with rejection region R is P(R|H_o is true) .

• A type I error occurs if you reject the null hypothesis when it is true.

Examples:

A person is arrested by the police in a stealing case, but he has not stolen anything. In this situation type I error is made.

H_o = He is innocent

H_a = He is not innocent 

In this situation the person has not stolen. But he is arrested by the police so H_o is reject although it (H_o) is correct so therefore Type-I Error is made.

Type II Error

Type II error, also known as a "false negative": the error of not rejecting a null hypothesis when the null hypothesis is false (alternative hypothesis is the true). In other words, this is the error of failing to accept an alternative hypothesis when you don't have adequate power. So the probability of making a type II error in a test with rejection region R is P(R|H_o is false).

• A type II error occurs if you do not reject the null hypothesis when it is false.

Examples:

A person has stolen anything but he is not arrested by the police. In this situation Type-II Error is made.

H_o = He is thief

H_a = He is not thief 

In this situation the person has stolen anything, but he is not arrested  by the police so H_o is not reject (H_a is accepted) although it is not correct so therefore Type-II Error is made.

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Hypothesis Testing (Null & Alternative)

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Hypothesis Testing

Hypothesis Testing

Any assumption or statement which can be tested and may or may not be true is called Hypothesis. The process of testing the statement or assumption is called Hypothesis Testing.

Examples:

• A new medicine you think might work.
• A way of teaching might be better.

Hypothesis testing in statistics is a way for you to test the results of a survey or experiment to see if you have meaningful results.
There are two types of hypothesis testing.

1. Null Hypothesis (Ho)
2. Alternative Hypothesis (Hi) 

1. Null Hypothesis (Ho)

Null Hypothesis (Ho) is a statistical hypothesis that states that there is no difference between a parameter and a specific value, or that there is no difference between two parameters.

Alternative Hypothesis (Hi or Ha)

Alternative Hypothesis (Hi or Ha) is a statistical hypothesis that states the existence of a difference between a parameter and a specific value, or states that there is a difference between two parameters.

Example: A publisher of college textbooks claims that the average price of all hardbound college textbooks is $127.50. A student group believes that the actual mean is higher and wishes to test their belief. State the relevant null and alternative hypotheses.

Solution:

The null hypothesis is Ho : μ = $127.50.

Since the student group thinks that the average textbook price is greater than the publisher’s figure.

The alternative hypothesis in this situation is Ha : μ > $127.50.

Tow Tailed Test

The Two Tailed Test is that test in which both side of the bell curve are the critical regions. As it is shown in the bellow examples.

Example: A psychologist feels that playing soft music during a test will change the results of the test. The psychologist is not sure whether the grades will be higher or lower. In the past, the mean of the scores was 73

Ho: µ = 73 and Hi: µ m ≠ 73

Right Tailed Test (One-tailed Test)

The Right Tailed Test is that test in which the critical regions are only right side of the bell curve. As it is shown in the bellow examples

Example: A chemist invents an additive to increase the life of an automobile battery. If the mean lifetime of the automobile battery without the additive is 36 months, then her hypotheses are

Ho: µ = 36 and Hi: µ  > 36

Left Tailed Test (One-tailed Test)

The Left Tailed Test is that test in which the critical regions are only left side of the bell curve. As it is shown in the bellow examples

Examples: A contractor wishes to lower heating bills by using a special type of insulation in houses. If the average of the monthly heating bills is $78, her hypotheses about heating costs with the use of insulation are

Ho: µ = $78 and Hi: µ  < $78

Hypothesis Testing Common Phrases

Hypothesis Testing, Null and Alternative Hypothesis

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Two Tailed, Right Tailed and Left Tailed Test

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Type I and Type II Errors

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