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

Level of significance, Level of Significance: α The main purpose of hyp...

Level of Significance: α The main purpose of hypothesis testing is not to question the computed value of the sample statistic, but to make judgment about the difference between

Evaluate the standard deviation, Use only the rare event rule, and make sub...

Use only the rare event rule, and make subjective estimates to determine whether events are likely. For example, if the claim is that a coin favors heads and sample results consis

What are the coefficients of the linear combination, For the following ques...

For the following questions we are interested in a comparison of the 16 years education vs. > 16 years. (Recall we did the analysis on the log scale, so these are actual means on t

Econometrics, The following data on calcium content of wheat are consistent...

The following data on calcium content of wheat are consistent with summary quantities that appeared in the article “Mineral Contents of Cereal Grains as Affected by Storage and Ins

#title., 1 Se toma una muestra de 81 observaciones con una desviación están...

1 Se toma una muestra de 81 observaciones con una desviación estándar de 5. La media de la muestra es de 40. Determine el intervalo de de confianza de 99% para la media

Combined standard deviation, How to a calculate the combined standard devia...

How to a calculate the combined standard deviation for five groups (samples)?

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

Recitilinear motion, velocity of a particle which moves along the s-axis is...

velocity of a particle which moves along the s-axis is given by v=2-4t+5t then find position velocity,acceleration

Multivariate statistical methods, As one of the oldest multivariate stati...

As one of the oldest multivariate statistical methods of data reduction, Principal Component Analysis (PCA)simplifies a dataset by producing a small number of derived

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