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

Heteroskedastic-consistent standard errors, The following table shows the r...

The following table shows the results of fitting a linear regression model of starting annual salaries on a constant, GPA (4 point scale), and a variable (Metrics =1) indicating wh

Descriptive statistics, Explanation of descriptive statistics Describe ...

Explanation of descriptive statistics Describe what these descriptive statistics show or what recommendations you would create to AIU.  What information do you now have as a re

Correlation, Correlation The correlation is commonly used and a useful...

Correlation The correlation is commonly used and a useful statistic used to describe the degree of the relationships between two or more variables. Pearson's correlation refle

Determine the probability, For a distribution of scores with = 82 and stand...

For a distribution of scores with = 82 and standard deviation = 2.5, find the following: (Don't forget to sketch the normal curve to help you visualize what you are trying to fi

Assignment 1: Testing Hypotheses for Means, Review the Learning Resources a...

Review the Learning Resources and the media programs related to t tests. For additional support, review the Skill Builder: Research Design and Statistical Design and the Skill Buil

Statistics assignment, To compare three brands of computer keyboards, four ...

To compare three brands of computer keyboards, four data entry specialists were randomly selected. Each specialist used all three keyboards to enter the same kind of text material

Exam, I need to know if the exam will be guarantee to pull my grade up to a...

I need to know if the exam will be guarantee to pull my grade up to a B or an A. I have a D right now so i need to get someone that is willing to put effort on completing it???

Determine the matrix of the transformation, Consider the linear transformat...

Consider the linear transformation (a) Find the image of (3 , -2 , 2) under T. (b) Does the vector (5, 3) belong to the range of T? (c) Determine the matrix of the transf

Calculate the standard deviation, Zinc is a trace element and it is importa...

Zinc is a trace element and it is important in wound healing, building up the immune system and DNA synthesis. The data in Table 1 represents the zinc intake (in milligrams) for a

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