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NOTES: sample proportions sampling distributions
A Simple Random Sample used to obtain p^ provides an unbiased estimator of p . In other words, the
mean of the sampling distribution of the p^ numbers is p . In notation:
Also, the standard deviation of the sampling distribution of the p^ numbers is given by (where n is the
sample size):
Conditions/Requirements:
Sample proportions ( p^ numbers) have a normal sampling distribution, with mean and standard deviation
formulas above, provided certain conditions are met:
1. The sample proportion p^ must be obtained from a Simple Random Sample (SRS).
2. 10?np . (Note that some books say that it is sufficient for 5?np .)
3. 10)1( ?? pn . (Note that some books say that it is sufficient for 5)1( ?? pn .)
4. The population size is at least ten times the sample size ( n ).
EXERCISES:
1. Suppose medical researchers think that 0.70 is the proportion of all teenagers with high blood
pressure who...

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