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

Aviation legislation - SUPPLEMENTAL TYPE CERTIFICATION, JAR 21 SUPPLEMENTAL...

JAR 21 SUPPLEMENTAL TYPE CERTIFICATION JAR 21 Part E introduces the need for Supplemental Type Certification when a manufacturer wishes to make major changes to the Type Desig

Flow chart for confidence interval, Flow Chart for Confidence Interval ...

Flow Chart for Confidence Interval We can now prepare a flow chart for estimating a confidence interval for μ, the population parameter. Figure

Compute the roughness of several parametric densities, An approximation to ...

An approximation to the error of a Riemannian sum: where V g (a; b) is the total variation of g on [a, b] de ned by the sup over all partitions on [a, b], including (a; b

Types of correlation, Type of Correlation 1.      Positive and Negat...

Type of Correlation 1.      Positive and Negative Correlation: 2.      Simple Partial and Multiple Correlations. 3.      Linear and  Non linear or Correlations

Correlation, prove that coefficient of correlation lies between -1 and+1

prove that coefficient of correlation lies between -1 and+1

Bionomial, The Quality Manager of a battery manufacturing plant reviewed th...

The Quality Manager of a battery manufacturing plant reviewed the warranty records within his department and found that 4% of the low maintenance batteries produced at the plant ov

Angle count method, Angle Count method The method for estimating the pr...

Angle Count method The method for estimating the proportion of the area of a forest which is in fact covered by the bases of trees. An observer goes to each of the number of po

Conduct a hypothesis testing, Celia is a nurse in a geriatric ward.  She no...

Celia is a nurse in a geriatric ward.  She noticed that older persons in her care are having problems sleeping at night.  She decided to introduce non-pharmocologic ways of relaxat

Break-even analysis, a. How can break-even analysis be used in selecting a ...

a. How can break-even analysis be used in selecting a new plant site? b. What are potential advantages and disadvantage of locating a production facility in foreign country i

Penman-monteith method, (a) Average rainfall during the month of January...

(a) Average rainfall during the month of January is found to be 58 mm. A Class A pan evaporation recorded an average of 8.12 mm/day near an irrigation reservoir. The average

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