Type i and ii errors, Applied Statistics

Assignment Help:

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.


Related Discussions:- Type i and ii errors

Estimate the standard deviation of the process, Estimate the standard devia...

Estimate the standard deviation of the process: Draw the X (bar) and R charts for the data given and give your comments about the process under study. Estimate the standard de

Corelation regrassion, the two regrassion line will pass through the point ...

the two regrassion line will pass through the point (x,y)

Type of variable in regression analysis, Type of Variable in Regression Ana...

Type of Variable in Regression Analysis There are two types of variable in regression analysis. These are: a.      Dependent variable b.      Independent variable

WEDGE FRICTION, Ask question #MinimumA wedge is small piece of material hav...

Ask question #MinimumA wedge is small piece of material having two of their opposite faces not parallel. To lift block of weight W, it is pushed by horizontal force P which lifts t

Chi-square test, Consider the following linear regression model:      a)...

Consider the following linear regression model:      a) What does y and x 1 , x 2 , . . . . x k represent?      b) What does β o , β 1 , β 2 , . . . . β k represent?

Data reduction, The PCA is amongst the oldest of the multivariate statistic...

The PCA is amongst the oldest of the multivariate statistical methods of data reduction. It is a technique for simplifying a dataset, by reducing multidimensional datasets to lower

Association of attributes, In an examination 600 candidates appeared, boys ...

In an examination 600 candidates appeared, boys outnumbered girls by 16% of all candidates. number of passed candidates exceeded the number of failed candidates by 310. Boys failin

Analysis of covariance (ancova), Analysis of covariance (ANCOVA) It is ...

Analysis of covariance (ANCOVA) It is initially used for an expansion of the analysis of variance which permits to the possible effects of continuous concomitant variables (suc

Asymmetric proximity matrices, Asymmetric proximity matrices Immediacy...

Asymmetric proximity matrices Immediacy matrices in which the off-diagonal elements which are, in the i th row and j th column and the j th row and i th column, are not essent

Che, Chebychev inequality

Chebychev inequality

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd