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

Use of statistical tool, #question what is the statistical process to redu...

#question what is the statistical process to reduce hardness of water

Eliminate all of the insignificant variables, The file Midterm Data.xls ha...

The file Midterm Data.xls has a tab labeled "Many vs. S&P" which presents historical price data for several assets, a volatility condition (VIDX = 1 if the NYSE volatility is grea

Use event rule ot estimates the claim, Make a decision about the given clai...

Make a decision about the given claim. Use only the rare event rule, and make subjective estimates to determine whether events are likely. For example, if the claim is that a coi

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

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

Decision theory, 1. Definition of decision tree, 2. Feature of decision the...

1. Definition of decision tree, 2. Feature of decision theory problem

Median for ungrouped data, If the data set contains an odd number of items,...

If the data set contains an odd number of items, the middle item of the array is the median. If there is an even number of items, the median is the average of the two items. If the

Age at first marrage, get a questionnaire that captured age at first marria...

get a questionnaire that captured age at first marriage

Small sample test for mean, If the sample size is less than 30, then we nee...

If the sample size is less than 30, then we need to make the assumption that X (the volume of liquid in any cup) is normally distributed. This forces    (the mean volume in the sam

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