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# Sampling distributions

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### Sampling distributions

1. 1. Sampling Distribution
2. 2. Vocabulary • • • • • • 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. 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. 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. 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