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Unformatted text preview: MST 2250  Lesson 20
The Sampling Distribution of the Proportion
March 11, 2011 Deﬁnition:
The sampling distriblgion of the proportion is the probability distribution of all possible
sample proportions ) of sample size n that could be drawn from a population. 1.) Sampling error: Ihe absolute value of the difference between a
sample proportion (39) and the true population proportion ($9 )t
Example: EAI Corporation. )500 managers. 60 % completed a
performance evaluation training program (p=0.6). I snort/(Mariel jgcpg pertains“)?
E i “J? enema ﬁﬂewrtgiﬂ“ “a at “MM is mi?“
[5’  arm 2‘) Point estimates: The sampie proportion If? ) is a point estimate of the
population proportion ﬁmwmaﬁ/wéﬁt? ﬁﬁﬁmwm Skmmﬂmﬁ ﬁe i“ f? wig“ ﬁfjﬂﬁ‘ L2OSampDistribProp 3.) Developing the sampling distribution: Example: LZOSampDi strimep vaative Frequency RELATIVE FREQUENCY HISTOGRAM OF [I VALUES FROM 500 SEMPLE
RANDOM SAMPLES OF SIZE 30 EACH ,40 ‘15 .10 .05 ,VL/r “WWWWWW_““K W a mum ,.,.,..umw LZOSampDistribProp m Properties of the sarpling distribution. «t/
M “W
5.) Standard error oft e proportion.
ﬁre 939
e37 #1 {Mo m w . W 50f\ J r
6;) The “Central Limit Theorem” if the sampie size n is sufﬁciently iarge then the sampiing distribution
of the proportion Wiii approximate a normai distriio‘ation no matter the
shape of the population. in this ease: rip must be greater than or equal to 5 grid nﬂnp} must be greater than or equai to 5 i am, U) Example Problems:
EAI Corporation; 500 managers. 60 % completed a performance evaluation training program (p=0.6). ‘
a) What is the probability of drawing a sample of 100 managers from
this population with a sample proportion within =/— 0.03 (or 3%) of \]
I
V 4.63: may \ A»: C: 3 b) If the sample size were increased to 200, what would this probability
be? L2OSampDistribProp ...
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This note was uploaded on 02/05/2012 for the course MGT 2250 taught by Professor Milne during the Summer '08 term at Georgia Institute of Technology.
 Summer '08
 Milne

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