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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