2. Vocabulary
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Sample – part of a population
Parameters – refer to the population 𝜇, 𝜎, 𝑝
Statistics – refer to the sample 𝑥, 𝑠, 𝑝
Population Proportion = p
Sample Proportion = 𝑝
Sampling Distribution = the distribution of the
sample means or sample proportions
3. Sample proportion vs Population
Proportion
• Suppose p = .64 (population proportion)
• We take 10 samples and find that their sample
proportions are:
• .53, .55, .58, .61, .63, .65, .65, .71, .72, .91
• As we take more and more samples our
sample proportions will begin to make a bellshaped curve centered around the true
population proportion of p=.64
4. Sampling Proportions
• 𝑝=
# 𝑠𝑢𝑐𝑐𝑒𝑠𝑠𝑒𝑠 𝑖𝑛 𝑠𝑎𝑚𝑝𝑙𝑒
# 𝑖𝑛 𝑠𝑎𝑚𝑝𝑙𝑒
= proportion statistic
• 𝑥 𝑝 = the mean of the sample proportions = p
– The mean of all of the sample proportions is equal
to the true population proportion
– We can rarely take all possible samples
– 𝜎𝑝 =
𝑝(1−𝑝)
𝑛
– We can only use this when 10n≤ 𝑁
5. Approximating to Normal Curve
• We can approximate 𝑝 to be Normal if the following
conditions are met
– np≥ 10
– n(1-p) ≥10
– 10n≤ 𝑁
We then can calculate a z-score for a specific sample
proportion against the population proportion
z-score =
𝑝−𝑝
𝜎
This gives the # of standard deviations the sample proportion is
from the population proportion.
You can therefore also find the probability of a sample proportion
occurring from the z-score
