We want to use our statistic to estimate the parameter – will our statistic be exactly the same as the population parameter? Recall the notion of sampling variability: Different samples from the same population may yield different values of the sample statistic. DEFINITION The sampling distribution of a statistic is the distribution of values taken by the statistic in all possible samples from the same population. CENTRAL LIMIT THEOREM (CLT) The sampling distribution of a sum or percentage will become approximately normal as the sample size gets larger.SAMPLING DISTRIBUTION OF THE SAMPLE PROPORTION Take a Simple Random Sample (SRS) of size n from a population that contains a certain true proportion of successes, p. Let pො be the sample proportion of successes. If the sample size is large enough, then a. The sampling distribution of pො is approximately normal b. The mean of this normal distribution is p c. The standard deviation of this distribution is
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