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random sampling question - I need help
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anthony11
science forum beginner


Joined: 02 Mar 2006
Posts: 11

PostPosted: Wed Mar 15, 2006 7:27 am    Post subject: random sampling question - I need help Reply with quote

A journalist wanted to learn the views of the chief executive officers of the 500 largest United States corporations on program trading of stocks. In the time available, it was only possible to contact a random sample of eighty-one of these chief executive officers. If 55% of all the population members believe that program trading should be banned, what is the probability that less than half the sample members hold this view?

Ans. 0.8159 (but I think it’s wrong)

I’ve been unable to attain this answer despite numerous attempts, I would really appreciate some help.
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Brian M. Scott
science forum Guru


Joined: 10 May 2005
Posts: 332

PostPosted: Wed Mar 15, 2006 9:15 pm    Post subject: Re: random sampling question - I need help Reply with quote

On Wed, 15 Mar 2006 02:27:29 EST, anthony
<anthonysull@hotmail.com> wrote in
<news:22197722.1142407680911.JavaMail.jakarta@nitrogen.mathforum.org>
in alt.math.undergrad:

Quote:
A journalist wanted to learn the views of the chief
executive officers of the 500 largest United States
corporations on program trading of stocks. In the time
available, it was only possible to contact a random
sample of eighty-one of these chief executive officers.
If 55% of all the population members believe that program
trading should be banned, what is the probability that
less than half the sample members hold this view?

Ans. 0.8159 (but I think its wrong)

Definitely wrong: the probability that less than 55% of the
sample members -- the expected value -- hold the view is
about 0.5, and the desired probability clearly has to be
smaller. (If my rough and ready calculations are right,
it's actually a little over 0.11.)

[...]

Brian
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Stan Brown
science forum Guru Wannabe


Joined: 06 May 2005
Posts: 279

PostPosted: Thu Mar 16, 2006 2:47 am    Post subject: Re: random sampling question - I need help Reply with quote

Wed, 15 Mar 2006 16:15:44 -0500 from Brian M. Scott
<b.scott@csuohio.edu>:
Quote:
On Wed, 15 Mar 2006 02:27:29 EST, anthony
anthonysull@hotmail.com> wrote in
news:22197722.1142407680911.JavaMail.jakarta@nitrogen.mathforum.org
in alt.math.undergrad:

A journalist wanted to learn the views of the chief
executive officers of the 500 largest United States
corporations on program trading of stocks. In the time
available, it was only possible to contact a random
sample of eighty-one of these chief executive officers.
If 55% of all the population members believe that program
trading should be banned, what is the probability that
less than half the sample members hold this view?

Ans. 0.8159 (but I think it?s wrong)

Definitely wrong: the probability that less than 55% of the
sample members -- the expected value -- hold the view is
about 0.5, and the desired probability clearly has to be
smaller. (If my rough and ready calculations are right,
it's actually a little over 0.11.)

My TI-83, using binomcdf(81, .55, 40), gives a probability of 0.1827.
I notice that this is very close to the complement of the wrong
answer of 0.8159 that was given, and therefore I wonder if there was
a typo somewhere.

--
Stan Brown, Oak Road Systems, Tompkins County, New York, USA
http://OakRoadSystems.com/
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anthony11
science forum beginner


Joined: 02 Mar 2006
Posts: 11

PostPosted: Wed Mar 22, 2006 12:07 am    Post subject: Re: random sampling question - I need help Reply with quote

Thank you guys for all of your help.
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