Type i and ii errors, Applied Statistics


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 

=        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.

Posted Date: 9/15/2012 3:16:26 AM | Location : United States

Related Discussions:- Type i and ii errors, Assignment Help, Ask Question on Type i and ii errors, Get Answer, Expert's Help, Type i and ii errors Discussions

Write discussion on Type i and ii errors
Your posts are moderated
Related Questions
method for solving assingnment problem

These techniques are applied when the rows and the columns of the data table represent the same units and when the measure is a disiance or a similarity. The goal of the analysis i

The Neatee Eatee Hamburger Joint specializes in soyabean burgers. Customers arrive according to the following inter - arrival times between 11.00 am and 2.00 pm: Interval-arrival

(1) Assume we categorize voters in a city as havingless educationand those havingmoreeducation. Those with less education have less than a college degree; those with more education

A file on DocDepot in the assignments folder on doc-depot called bmi.mtp contains data on the Body Mass Index (BMI) of a population of Ottawa residents. The first column identifies

10. If a set of scores has a sample mean of 25 and a sample variance of 4, find the following: a. the z-score for a raw score of 31 b. the z-score for a raw score of 18 c. the raw

Let X 1  and X 2  be two independent populations with population means μ 1  and  μ 2  respectively. Two samples are taken, one from each population, of sizes n 1  and n 2  re

Convenience Sampling It means a convenient sample is obtained by selecting convents units from the universe. Convenient sample is also known as chunk. It   means a fraction of

Apl.send me nots on hypothesis testing sk question #Minimum 100 words accepted#

MARKS IN LAW :10 11 10 11 11 14 12 12 13 10 MARKS IN STATISTICS :20 21 22 21 23 23 22 21 24 23 MARKS IN LAW:13 12 11 12 10 14 14 12 13 10 MARKS IN STATISTICS:24 23 22 23 22 22 24 2