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When you perform a hypothesis test, there are four possible outcomes depending on the actual truth (or falseness) of the null hypothesis H 0 and the decision to reject or not. The outcomes are summarized in the following table:

True False
Cannot reject H 0 Correct Outcome Type II error
Cannot accept H 0 Type I Error Correct Outcome

The four possible outcomes in the table are:

  1. The decision is cannot reject H 0 when H 0 is true (correct decision).
  2. The decision is cannot accept H 0 when H 0 is true (incorrect decision known as a Type I error ). This case is described as "rejecting a good null". As we will see later, it is this type of error that we will guard against by setting the probability of making such an error. The goal is to NOT take an action that is an error.
  3. The decision is cannot reject H 0 when, in fact, H 0 is false (incorrect decision known as a Type II error ). This is called "accepting a false null". In this situation you have allowed the status quo to remain in force when it should be overturned. As we will see, the null hypothesis has the advantage in competition with the alternative.
  4. The decision is cannot accept H 0 when H 0 is false ( correct decision whose probability is called the Power of the Test ).

Each of the errors occurs with a particular probability. The Greek letters α and β represent the probabilities.

α = probability of a Type I error = P (Type I error) = probability of rejecting the null hypothesis when the null hypothesis is true.

β = probability of a Type II error = P (Type II error) = probability of not rejecting the null hypothesis when the null hypothesis is false.

α and β should be as small as possible because they are probabilities of errors.

Statistics allows us to set the probability that we are making a Type I error. The probability of making a Type I error is α. Recall that the confidence intervals in the last unit were set by choosing a value called Z α (or t α ) and the alpha value determined the confidence level of the estimate because it was the probability of the interval capturing the true mean (or proportion parameter p). This alpha and that one are the same.

The easiest way to see the relationship between the alpha error and the level of confidence is with the following figure.


In the center of [link] is a normally distributed probability distribution marked Ho. This is a sampling distribution of X and by the Central Limit Theorem it is normally distributed. The distribution in the center is marked H 0 and represents the distribution for the null hypotheses H 0 : µ = 100. This is the value that is being tested. The formal statements of the null and alternative hypotheses are listed below the figure.

The distributions on either side of the H 0 distribution represent distributions that would be true if H 0 is false, under the alternative hypothesis listed as H a . We do not know which is true, and will never know. There are, in fact, an infinite number of distributions from which the data could have been drawn if H a is true, but only two of them are on [link] representing all of the others.

Questions & Answers

what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
Do somebody tell me a best nano engineering book for beginners?
s. Reply
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
many many of nanotubes
what is the k.e before it land
what is the function of carbon nanotubes?
I'm interested in nanotube
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
preparation of nanomaterial
Victor Reply
how to synthesize TiO2 nanoparticles by chemical methods
what's the program
what chemical
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Business statistics -- bsta 200 -- humber college -- version 2016reva -- draft 2016-04-04. OpenStax CNX. Apr 05, 2016 Download for free at http://legacy.cnx.org/content/col11969/1.5
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