reasoning is subject to error and can be influenced by social factors
and beliefs.we also tend to test conclusions for hypotheses by
examining only evidence that we expect will confirm them.what is this
phenomenon reffered to,and what is an every day example?

One explanation is dissonance reduction.  If our beliefs are not
confirmed, this causes 'cognitive dissonance' - which we do not like.
http://psychology.rutgers.edu/Users/kharber/socialpsychclass14.html
http://www.marketing.org.au/papers/consumer.htm
http://vassun.vassar.edu/~laotoole/final%20project/main%20page.html
Says "cognitive dissonance, conflict reduction, self-concept - We make
choices that will reduce or eliminate any inner-conflict and make us
feel good about ourselves (Leippe & Eisenstadt, 1994)."

Of course, having our beliefs and hypotheses disconfirmed makes us
uncomfortable, so we try to stop it happening, by only seeking
evidence that confirms it.

Search terms:
confirm beliefs cognitive dissonance
 dissonance reduction belief confirmation
://www.google.com/search?q=dissonance+reduction++belief+confirmation
"dissonance reduction" confirming beliefs
://www.google.com/searchq=%22dissonance+reduction%22+confirming+beliefs

An everyday example is post-consumer behaviour and advertising.  That
is, you want to have the hypothesis confirmed that you made the
correct decision.  The best place to find this is in adverts for the
product you bought, so you read those adverts.

http://www.ciadvertising.org/studies/student/99_fall/theory/blakeman/Theories/prin.html

Search terms:
dissonance adverts OR advertisements 

://www.google.com/search?q=dissonance+adverts+OR+advertisements

You will find more examples in a social psychology textbook.  My
particular favourite is "The Social Animal" by Eliot Aronson, but
there are lots of others.

I hope that has answered your question,

jeremymiles-ga

Recommend "Decision Traps" by Russo.

Good luck !

I think what you're talking about is selective perception. 
jeremymiles-ga did a good job of describing one theory as to why
selective perception occurs.  The easiest way for me to understand the
phenomenon is that we have a certain way of looking at the world,
psychologists refer to this psychological/perceptual framework a
schema.  Our schema serves as a foundation for our understanding of
how the world works, and in the simplest sense, you can think of a
schema as a collection of a person's points of view. People tend to be
heavily psychologically invested in maintaining their schemata
(schemata is the plural for schema.  I know... it's weird), because
without a framework for understanding how the world works, society
pretty confusing.  Because we have a schema, we're predisposed to see
things in a certain way.  A predisposition to see things in a
particular way is the foundation of selective perception.

A quote from alleydog
http://www.alleydog.com/glossary/definition.cfm?term=Schema

"Schema: A cognitive system which helps us organize information. For
example, you may have a conceptual framework or developed a schema
that all homeless people are rude. Because of this schema, you
organize your actions around it and more readily look for information
that supports this view while discarding information that disagrees
with this perspective. Schemas exert a great deal of influence over us
and sometimes hinder us from remembering new information because it
does not fit into our cognitive framework."

Another example: Take 3 workers named Bob, Greg, and Susan.  The day
that Bob started, he was a little sick, and was curt with Greg.  For
this reason, Greg thinks that Bob is snooty and doesn't like him at
all. Bob. Susan, who sits on the other side of Bob, was out of the
office when Bob started, and met him after work one day on the
elevator.  Bob was totally pleasant, but really shy.  Bob comes to
work every morning, doesn't say "hi" to anyone, goes in his office and
closes the door.  Greg and Susan see Bob every morning walking in, 
and although they see the exact same thing, their perception of the
event is radically different.  Greg thinks that Bob is aloof and rude.
 Susan thinks that Bob is shy and nice.  Actually, Susan kind of likes
shy guys, and as she's had little actual contact with Bob, she's
filled in the blanks herself and privately has a little crush on him.

This example is pretty simplified, but illustrates the basic point.

Thanks to Misterheavy-ga for the additional information.  We are
talking about the same (sort of) thing from two different perspectives
- I was addressing the issue from a social psychological sort of
approach, whereas misterheavy was approaching it from a cognitive
psychological sort of approach.  These two have met in the middle, to
form a branch of psychology called 'social cognition'.  You might want
to look into the work of J. Richard Eiser, who has done work on
attitudes, computation and neural networks.  He has done computer
simulations and found that neural nets can have a sort of confirmation
bias.  His web page, which contains links to his publications, is
here;
http://www.shef.ac.uk/uni/academic/N-Q/psology/staff/eiserd.shtml

I have learned that this phenomenon is known as the "confirmation
bias", as briefly mentioned at the end of one of jeremymiles'
comments. It is defined as a bias (tendency) to seek out evidence that
confirms (supports) your currently held beliefs.

A confirmation bias may be used as a means of dissonance reduction,
but I personally think "dissonance reduction" refers to a category of
behaviors, rather than this one phenomenon. The term "selective
perception" was used by misterheavy, which is an okay phrase provided
that it is grounded in the present context, because selective
perception can also refer to many other psychological phenomena (e.g.,
attention). I do not agree, however, with misterheavy's office worker
example. Although the co-workers perceive Bob in different ways based
on their experiences with him, there was no attempt to confirm a
pre-existing belief. There is really no opportunity for cognitive
dissonance, thus, no confirmation bias.

Here is an extension of the example that I feel is more pertinent:
John also works in the office with Bob, Susan, and Greg. He has heard
rumours that Bob is not very friendly, but wants to know for sure. He
is aware that Greg has voiced negative feelings about Bob and that
Susan seems to be okay with him, but John only asks Greg for his
opinion. Naturally, Greg expresses his dislike for Bob, confirming
John's belief that Bob is not very friendly. By only asking Greg
(i.e., seeking out information to confirm his beliefs), John is
displaying a confirmation bias.

I don't think the office worker example is the best illustration of
the confirmation bias, however, so here's another one: A researcher
thinks that red light is best for optimum plant growth. He conducts a
simple experiment with two plants, one under normal (white) light and
one under red light. Let's say the red light plant grows better. The
researcher concludes that red light is best for plant growth. There
exists a confirmation bias, however, if the researcher does not go
further and look at the effects of other colored lights (blue, green,
etc). He only considered and sought out evidence to confirm his
beliefs, with looking at the broader range of possibilities.

Another short example: Someone wants to show that all drugs are
detrimental to one's health. So he does a literature search for
"negative effects of drugs" and comes up with a whole bunch of
information that supports his belief and subsequently writes his paper
saying that all drugs are bad. The confirmation bias, however, is that
he only looked for information that would potentially support, not
refute, his position.

Hopefully this helps the questioner out. A Google search for
"confirmation bias" will produce a lot of related links. The above
information was from personal knowledge.