Type i and ii errors, Applied Statistics

TYPE I AND II Errors

If a statistical hypothesis is tested, we may get the following four possible cases:

  1. The null hypothesis is true and it is accepted;

  2. The null hypothesis is false and it is rejected;

  3. The null hypothesis is true, but it is rejected;

  4. The null hypothesis is false, but it is accepted.

Clearly, the last two cases lead to errors which are called errors of sampling. The error made in (c) is called Type I Error. The error committed in (d) is called Type II Error. In either case a wrong decision is taken.

P(Committing a Type I Error)

=       P (The Null Hypothesis is true but is rejected)\

=       P (The Null Hypothesis is true but sample statistic falls in the rejection region)

=    α, the level of significance

P(Committing a Type II Error)

=       P (The Null Hypothesis is false but sample statistic falls in the acceptance 
         region)

=        β (say)

The level of significance,   α , is known. This was fixed before testing started.   β is known only if the true value of the parameter is known. Of course, if it is known, there was no point in testing for the parameter.

Posted Date: 9/15/2012 3:16:26 AM | Location : United States







Related Discussions:- Type i and ii errors, Assignment Help, Ask Question on Type i and ii errors, Get Answer, Expert's Help, Type i and ii errors Discussions

Write discussion on Type i and ii errors
Your posts are moderated
Related Questions
CALCULATE THE PERCENTAGE OF REFUNDS EXPECTED TO EXCEED $1000 UNDER THE CURRENT WITHHOLDING GUIDELINES



Assume that a simple random sample has been selected from a normally distribute population and test the given claim. Identify the null and alternative hypotheses, test statistic,

Having 11 numbered balls -0 to 10 -into a basket and have 6 spaces to be numbered with the balls selected in each 6 chances and it returned it back to the basket each time. Chanc

An approximation to the error of a Riemannian sum: where V g (a; b) is the total variation of g on [a, b] de ned by the sup over all partitions on [a, b], including (a; b

how can we use measurement error method with eight responses variables (we do not have explanatory variable in the data )?.the data analyse 521 leaves ..

A researcher was interested lowering the high school dropout level in his county. He measured the reading level of students entering middle school (based on a standard test) and th

Methods of Forecasting  Various techniques which are generally used in business forecasting are as under: 1.      Forecasting  through the opinion of heads  of department

Problem : A company supplying electrical products, places a rush order for electric wires. Consignments of wires are to be sent immediately when they are available. Previous