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

Correlation - cause and effect, Cause and Effect Even a highly signifi...

Cause and Effect Even a highly significant correlation does not necessarily mean that a cause and effect relationship exists between the two variables. Thus, correlation does

Interpolation and extrapolation, Meaning of Interpolation and Extrapolation...

Meaning of Interpolation and Extrapolation Interpolation is a method of estimating the most probable  missing figure on  the basis of given data under certain assumptions. On t

What are the charateristics of a population for which, what are characteris...

what are characteristics of a population for which it would be appropiate to use mean/median/mode

Regression analysis, Meaning and Definitions of Regression The dictiona...

Meaning and Definitions of Regression The dictionary meaning of regression is just opposite the meaning of progression. Progression means to move forward while regression means

Steps in anova, Steps in ANOVA The three steps which constitute the ana...

Steps in ANOVA The three steps which constitute the analysis of variance are as follows: To determine an estimate of the population variance from the variance that exi

Bernoulli''s theorem, Bernoulli's Theorem If a trial of an experiment c...

Bernoulli's Theorem If a trial of an experiment can result in success  with probability p and failure with probability q (i.e.1-p) the probability of exactly r success in n tri

Classification of universe, Classification of Universe The universe may...

Classification of Universe The universe may be classified either on the basis of number of units and on the basis   of existence of units as is clear from the following chart :

business forecasting, Explain the characteristics of business forecasting

Explain the characteristics of business forecasting.

Evaluate the probability, "MagTek" electronics has developed a smart phone ...

"MagTek" electronics has developed a smart phone that does things that no other phone yetreleased into the market-place will do. The marketing department is planning to demonstrate

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