9 Pages

Statistical Sciences
Course Code
Statistical Sciences 2035
Steve Kopp

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The Sampling Distribution of the Sample Proportion (section 6.2) Studies often examine categorical data • categorical data consists of counts (x) or percents (proportions, p) obtained from counts • in chapter 7 and 8, we will want to calculate confidence intervals and test hypothesis for proportions • to do this, we first need to know the sampling distribution of p Consider the following Select a random sample of size n from a population and record the count, x, of “successes” x ~ Bin( n, p) where p = probability of success We are interested in estimating p, as it is often unknown To do this, we use our sample and calculate the sample proportion of success x p = n This is our point estimate of p Sampling Distribution of p Since p is calculated from our sample data, it is a statistic, • since it is a statistic, it has a sampling distribution associated with it In other words, suppose we repeat our experiment 10,000 times • take 10,000 random samples of size n • each time we calculate the sample ˆ proportion of success, p • we will get 10,000 values of p , some of them the same, but most of them different p • if we graph these 10,000 values of , what would the graph look like? 1. Centre If you took the 10,000 values of pˆ, added them up and divided by 10,000 you would get p µ = p In othe
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