# 5.1 Hypothesis testing of single mean and single proportion: null

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The actual test begins by considering two hypotheses . They are called the null hypothesis and the alternate hypothesis . These hypotheses contain opposing viewpoints.

${H}_{o}$ : The null hypothesis: It is a statement about the population that will be assumed to be true unless it can be shown to be incorrect beyond a reasonable doubt.

${H}_{a}$ : The alternate hypothesis: It is a claim about the population that is contradictory to ${H}_{o}$ and what we conclude when we reject ${H}_{o}$ .

${H}_{o}$ : No more than 30% of the registered voters in Santa Clara County voted in the primary election.

${H}_{a}$ : More than 30% of the registered voters in Santa Clara County voted in the primary election.

We want to test whether the mean grade point average in American colleges is different from 2.0 (out of 4.0).

${H}_{o}$ : $\mu =2.0\phantom{\rule{20pt}{0ex}}$ ${H}_{a}$ : $\mu \ne 2.0$

We want to test if college students take less than five years to graduate from college, on the average.

${H}_{o}$ : $\mu \ge 5\phantom{\rule{20pt}{0ex}}$ ${H}_{a}$ : $(\mu , 5)$

In an issue of U. S. News and World Report , an article on school standards stated that about half of all students in France, Germany, and Israel take advanced placementexams and a third pass. The same article stated that 6.6% of U. S. students take advanced placement exams and 4.4 % pass. Test if the percentage of U. S. students who take advancedplacement exams is more than 6.6%.

${H}_{o}$ : $p$ $=0.066\phantom{\rule{20pt}{0ex}}$ ${H}_{a}$ : $p$ $>0.066$

Since the null and alternate hypotheses are contradictory, you must examine evidence to decide if you have enough evidence to reject the null hypothesis or not. The evidence is in the form of sample data.

After you have determined which hypothesis the sample supports, you make a decision. There are two options for a decision. They are "reject ${H}_{o}$ " if the sample information favors the alternate hypothesis or "do not reject ${H}_{o}$ " or "fail to reject ${H}_{o}$ " if the sample information is insufficient to reject the null hypothesis.

Mathematical Symbols Used in ${H}_{o}$ and ${H}_{a}$ :

${H}_{o}$ ${H}_{a}$
equal ( $=$ ) not equal ( $\ne$ ) or greater than ( $>$ ) or less than ( $()$ )
greater than or equal to ( $\ge$ ) less than ( $()$ )
less than or equal to ( $\le$ ) more than ( $>$ )

${H}_{o}$ always has a symbol with an equal in it. ${H}_{a}$ never has a symbol with an equal in it. The choice of symbol depends on the wording of the hypothesis test. However, be aware that many researchers (including one of the co-authors in research work) use $=$ in the Null Hypothesis, even with $>$ or $<$ as the symbol in the Alternate Hypothesis. This practice is acceptable because we only make the decision to reject or not reject the Null Hypothesis.

## Optional collaborative classroom activity

Bring to class a newspaper, some news magazines, and some Internet articles . In groups, find articles from which your group can write a null and alternate hypotheses. Discuss yourhypotheses with the rest of the class.

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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