distribucio normal, Apuntes de Estadística

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STATISTICS

Degree in Psychology

Academic year 2011 – 2012

UNITS 1 & 2

SAMPLING DISTRIBUTION

SAMPLING DISTRIBUTION OF A

STATISTIC

Suppose we have a population that we extract, at

random, infinite samples of size n.

Then, in each sample is possible to determine the

value of any statistic (percentage, mean, etc.).

A sampling distribution is the set formed by the

values of the chosen statistic, obtained in each of

the samples taken from the original population.

SAMPLING DISTRIBUTION OF A

STATISTIC

It is a theoretical distribution that

assigns a probability to each of the

specific values that can take a statistic

in all samples of the same size that can

be extracted from the studied

population.

CENTRAL LIMIT THEOREM

Selection of random samples of n observations from a population with mean  and standard deviation   When n is large, the sampling distribution of the mean tends to a normal distribution with mean equal to  and standard error of /  Getting more accurate as n increases n

Inference: Sampling distribution

Parameters: Mean:   Variance: 2  

Main Sampling Distributions

Main Sampling Distribution

• (^) Proportions

n ·  & n · (1 - )  5

Mean: Standard error: N unknown N known

• (^) Means Mean: Standard error: N unknown N known    p   n p       1

1 1       N N n n p       x n x     1    N N n n x  

Example sampling distribution of the proportion

n = 50; p(p < 0,20) =?

p(p < 0,20) = 0,

 (early insomnia) = 0,

n

p

z

i

WEB Pages

http://descartes.cnice.mecd.es/Bach_HCS_2/ inferencia_estadistica/distrib_muestrales.htm http://www.hrc.es/bioest/esti_medias.html http://www.itch.edu.mx/academic/industrial/estadistica1/ cap01b.html http://www.itchihuahuaii.edu.mx/academico/CB/MEG/ documentos/1.6.htm http://people.hofstra.edu/faculty/Stefan_waner/RealWorld/ finitetopic1/sampldistr.html http://www.stat.tamu.edu/stat30x/notes/node77.html http://www.ruf.rice.edu/~lane/stat_sim/sampling_dist/ http://www.jcu.edu/math/ISEP/CLT/CLT.html http://www.tc.umn.edu/~delma001/stat_tools/ http://www.jcu.edu/math/ISEP/Quincunx/Quincunx.html http://www.stat.sc.edu/~west/javahtml/CLT.html http://descartes.cnice.mecd.es/3_eso/Azar_y_probabilidad/ azar_probabilidad_2.htm