AP Stat - Sampling Distribution - DHS

S.D. of sample distribution of proportion = ((p(1-p))/n)^1/2 IF…

population is 10 times larger than sample

Shape of sampling distribution of p-hat is normal when…

np >=10 and n(1-p) >=10

Statistics

A number that describes some characteristic of a sample

Parameter

A number that describes some characteristic of a population

Sample Statistics

x-bar, p-hat, s_x

Population Parameters

mu, p, sigma

Sample distribution statistics estimate…

population parameters

Sampling Variability

Different random samples of the same size from the same population produce different values for a statistic

Sampling Distribution

The distribution of values taken by the statistic in all possible samples of the same size from the same population

Unbiased estimator

The mean of the sampling distribution is equal to the value of the parameter being estimated

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In a particular sample the value may not be the same, but statistic will not consistently over or under estimate

The sampling distribution of the sample proportion (p-hat) describes…

the distribution of values taken by the sample proportion (p-hat) in all possible samples of the same size form the sample population

Larger sample sizes tend to have…

smaller variability of the sampling distribution

If the population is normally distributed…

the sample is normally distributed

If the sample is normally distributed..

this tells us nothing