P hat= Count of successes in sample   =  X
                         Size of sample                 N

X and P hat are Random Variables- this is going to change from sample to sample.

Mean of Sampling Distribution:

Fact~ The standard deviation of p-hat gets smaller when n(sample size) gets larger!           P-hat is less variable in large samples
 

Things to Check For...
N>10n
np>10
n(1-p)>10
**Dont Forget to Verify These Conditions!**

Steps...
Verify
Construct Interval
Interpret the Solution

Example:
(page 507)

We selected an SRS of 1500 first year college students and asked then whether they applied for admission to other colleges. In fact, 35% of first year college students apply to more than one school.  We want the probability that if an SRS of 1500 students that p-hat will fall within 2% points of true value.  (.33<p<.37)

Verify:
SRS- We are told that the data comes from a Simple Random Sample.
N>10n   10(1500)=15,000 There are more than 15,000 first year college students.
np>10    525>10
n(1-p)>10  975>10

Find the Standard Deviation:  the standard deviation = 
.35(.65)= .0123
   1500

P(.33<p<.37) use this formula 

P(.33-.35 < Z < .37-.35) = -1.63 < z < 1.63
     .0123           .0123

You need to use Table A to find the area to the left of each z score.  You can see them labeled above.  Now you must subtract .0516 from .9484 to find the area in the middle.

.9484-.0516= .8963

Interpret:
About 90% of all samples will give a result within 2% points from the mean.
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