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

Assumptions in anova, Assumptions in ANOVA The various populations f...

Assumptions in ANOVA The various populations from which the samples are drawn should be normal and have the same variance. The requirement of normality can be discarded if t

Difference between correlation and regression analysis, Difference between ...

Difference between Correlation and Regression Analysis 1. Degree and Nature  of Relationship: Coefficient of correlation measures   the degree  of covariance  between two vari

Mean deviation, First Moment of Dispersion or Mean Deviation Mean devia...

First Moment of Dispersion or Mean Deviation Mean deviation or the average deviation is the measure if dispersion which   is based upon all the items in a variable .It is the a

Correlation, Definition of Correlation According  to prof, king correla...

Definition of Correlation According  to prof, king correlation means that between two series or group  of data  there  exists  some casual connection  prof, king  has also  exp

Pattie-lynns utility function, Pattie-Lynn's utility function for total as...

Pattie-Lynn's utility function for total assets is, in which A represents total assets in thousands of dollars. (a) Graph Pattie-Lynn's utility function. How would y

Inference on reggression analysis, find the expected value of the mean squa...

find the expected value of the mean square error and of the mean square reggression

Calculate the length of the rope, The tension, T, in the tow rope pulling t...

The tension, T, in the tow rope pulling the car in Newtons is given in P8.  Determine the minimum length of the rope l, between A and B, so that the tension in either AB or AC equa

Scatter diagram - correlation analysis, Scatter Diagram The first step ...

Scatter Diagram The first step in correlation analysis is to visualize the relationship. For each unit of observation in correlation analysis there is a pair of numerical value

Construct a cumulative percentage polygon, 1. For each of the following var...

1. For each of the following variables: major, graduate GPA, and height: a. Determine whether the variable is categorical or numerical. b. If the variable is numerical, deter

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