# 9.2 Outcomes and the type i and type ii errors

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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 ${H}_{o}$ and the decision to reject or not. The outcomes are summarized in the following table:

ACTION ${H}_{o}$ IS ACTUALLY ...
True False
Do not reject ${H}_{o}$ Correct Outcome Type II error
Reject ${H}_{o}$ Type I Error Correct Outcome

The four possible outcomes in the table are:

• The decision is to not reject ${H}_{o}$ when, in fact, ${H}_{o}$ is true (correct decision).
• The decision is to reject ${H}_{o}$ when, in fact, ${H}_{o}$ is true (incorrect decision known as a Type I error ).
• The decision is to not reject ${H}_{o}$ when, in fact, ${H}_{o}$ is false (incorrect decision known as a Type II error ).
• The decision is to reject ${H}_{o}$ when, in fact, ${H}_{o}$ 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 $\alpha$ and $\beta$ represent the probabilities.

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

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

$\alpha$ and $\beta$ should be as small as possible because they are probabilities of errors. They are rarely 0.

The Power of the Test is $1-\beta$ . Ideally, we want a high power that is as close to 1 as possible. Increasing the sample size can increase the Power of the Test.

The following are examples of Type I and Type II errors.

Suppose the null hypothesis, ${H}_{o}$ , is: Frank's rock climbing equipment is safe.

Type I error : Frank thinks that his rock climbing equipment may not be safe when, in fact, it really is safe. Type II error : Frank thinks that his rock climbing equipment may be safe when, in fact, it is not safe.

$\alpha$ = probability that Frank thinks his rock climbing equipment may not be safe when, in fact, it really is safe. $\beta$ = probability that Frank thinks his rock climbing equipment may be safe when, in fact, it is not safe.

Notice that, in this case, the error with the greater consequence is the Type II error. (If Frank thinks his rock climbing equipment is safe, he will go ahead and use it.)

Suppose the null hypothesis, ${H}_{o}$ , is: The victim of an automobile accident is alive when he arrives at theemergency room of a hospital.

Type I error : The emergency crew thinks that the victim is dead when, in fact, the victim is alive. Type II error : The emergency crew does not know if the victim is alive when, in fact, thevictim is dead.

$\alpha$ = probability that the emergency crew thinks the victim is dead when, in fact, he is really alive = $\text{P(Type I error)}$ . $\beta$ = probability that the emergency crew does not know if the victim is alive when, in fact, the victim is dead = $\text{P(Type II error)}$ .

The error with the greater consequence is the Type I error. (If the emergency crew thinks the victim is dead, they will not treat him.)

where we get a research paper on Nano chemistry....?
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
how did you get the value of 2000N.What calculations are needed to arrive at it
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1 It is estimated that 30% of all drivers have some kind of medical aid in South Africa. What is the probability that in a sample of 10 drivers: 3.1.1 Exactly 4 will have a medical aid. (8) 3.1.2 At least 2 will have a medical aid. (8) 3.1.3 More than 9 will have a medical aid.