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

Index number, give a elementary example for characterstics of index number

give a elementary example for characterstics of index number

X-bar charts, First we look at these charts assuming that we know both the ...

First we look at these charts assuming that we know both the mean and the standard deviation of the process, that is  μ and  σ . These values represent the acceptable values (bench

Time series, Year Production 2006 8 2007 6 2008 10 2009 12 2010 11 2011 15 ...

Year Production 2006 8 2007 6 2008 10 2009 12 2010 11 2011 15 2012 14 2013 16 Determine the trend from data given above?

Inverse cumulative distribution function, The Null Hypothesis - H0: β0 = ...

The Null Hypothesis - H0: β0 = 0, H0: β 1 = 0, H0: β 2 = 0, Β i = 0 The Alternative Hypothesis - H1: β0 ≠ 0, H0: β 1 ≠ 0, H0: β 2 ≠ 0, Β i ≠ 0      i =0, 1, 2, 3

Regression lines, Regression Lines It has already been discussed that t...

Regression Lines It has already been discussed that there are two regression lines and they show mutual relationship between two variable . The regression line Yon X gives   th

Analysis of variance for the data, Analysis of Variance for the data: ...

Analysis of Variance for the data: Draw a random sample of size 25 from the following data : (a) With Replacement and   (b) Without Replacement and obtain Mean and Varia

Variance, Variance The term variance was used to describe the square of...

Variance The term variance was used to describe the square of the standard deviation by R.A.Fisher. The concept of variance is highly important in areas where it is possible to

Test the null hypothesis, A consumer preference study involving three diffe...

A consumer preference study involving three different bottle designs (A, B, and C) for the jumbo size of a new liquid detergent was carried out using a randomized block experimenta

Calculation of degrees of freedom, Calculation of Degrees of Freedom Fi...

Calculation of Degrees of Freedom First we look at how to calculate the number of DOF for the numerator. In the numerator since we calculate the variance from the sample means,

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