PSYC227_fall09_week7

# PSYC227_fall09_week7 - Normal Distribution Find probability...

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Normal Distribution 1. Sketch the distribution 2. Transform X values into z- scores 3. Use the unit normal table P(X < 130) = ? Find probability associated with individual scores (X values)

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2 Normal Distribution
3 Normal Distribution

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binomial normal Normal approximation to Binomial pn & qn both large (>10) Find probability associated with individual scores (X values)
5 The Distribution of Sample Means

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6 The Distribution of Sample Means Find probability associated with sample of scores (M values) What is the probability of selecting a random sample of scores with a sample mean less than 130? P( X < 130) = ? What is the probability that a randomly selected individual has a score less than 130? P( M < 130) = ? Previously, single score: Sample of scores:
Learning Objectives: 1. Define the distribution of sample means (shape, expected value of M, and the standard error of M). 2. Determine a location of a sample mean M in the distribution of sample means (z). 3. Compute probabilities corresponding to specific sample means. 4. Standard error The Distribution of Sample Means

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Definitions A sampling distribution is a distribution of statistics obtained by selecting all the possible samples of a specific size from a population. S ampling error is the discrepancy between a sample statistic and its corresponding population parameter. The distribution of sample means is the collection of sample means for all the possible samples of a specific size ( n ) from a population. It is an example of a sampling distribution.
Population of 4 scores : 2, 4, 6, 8 All possible samples of size n=2 The distribution of sample means for n=2

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Population of 4 scores : 2, 4, 6, 8 All possible samples of size n=2 The distribution of sample means for n=2 What is the probability of obtaining a sample mean greater than 6? P(M > 6) = 3/16
Uniform distribution N = 1,000 µ = 0.4938 σ 2 = 0.0805 σ = 0.2837 µ = 0.49 σ = 0.28

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Ten samples of n =5 measurements from a Uniform Distribution Sample Measurements Mean 1 0.6190 0.2218 0.8729 0.9981 0.8789 0.7181 2 0.9508 0.9391 0.8545 0.1780 0.1159 0.6077 3 0.1001 0.5180 0.9060 0.1286 0.8773 0.5060 4 0.5648 0.7494 0.7289 0.5531 0.4311 0.6055 5 0.2538 0.1965 0.9153 0.5500 0.3585 0.4548 6 0.4485 0.3013 0.0384 0.5178 0.6637 0.3939 7 0.1438 0.3667 0.4006 0.4485 0.4311 0.3581 8 0.8083 0.1453 0.3904 0.1393 0.4272 0.3821 9 0.6139 0.7624 0.9620 0.7658 0.5701 0.7348 10 0.7128 0.2487 0.2503 0.9586 0.0529 0.4447 M = 0.5206 µ = 0.49 σ = 0.28