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Statistics Assignment Help With Errors In Sampling

10.6 Errors In Sampling:

The main objective in sampling theory is to draw valid inferences about the population parameters on the basis of the sample results. In practice we decide to accept or reject the lot after examining a sample from it. As such we are liable to commit the following two types of errors:

Type I Error: Reject H0 when it is true.

Type II Error: Accept H0 when it is wrong, that is accept H0 when H1 is true.

If we write.

P { Reject H0 when it is true} = P{ Reject H0| H0} =α

and P { Accept H0 when it is wrong} = P{ accept H0| H1} =β

then α and β are called the sizes of type I error and type II error, respectively.

In practice, type I error amounts to rejecting a lot when it is good and type II error may be regarded as accepting the lot when it is bad.

Thus P { Reject a lot when it is good} = α

and P { Accept a lot when it is bad } = β

where α and β are referred to as Producer’s risk and consumer’s risk respectively.

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