Chapter 11 %28pages 153 -171%29

# Chapter 11 %28pages 153 -171%29 - MSIT 3000 Chapter 11...

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MSIT 3000 Chapter 11 Confidence Intervals and Hypothesis Tests for Means Section 11.1 Sampling Distributions for Means What other distributions have we talked about? How do we describe distributions? Previously, we’ve examined data and calculated statistics. The distributions were about data. Now we’ll consider the distribution, sampling distribution, that is associated with the statistic, y . This statistic has a distribution with a shape, center and variation. This distribution provides probabilities for the possible values of the statistic. 153

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Class Exercise: Working in pairs, toss a die 5 times. Record the number of dots on each of the 5 tosses, and calculate the average number of dots for the 5 tosses. Toss 1 2 3 4 5 Average # dots We will look at the THREE different distributions that are part of this exercise. Population Distribution : The distribution from which we took our sample. Data Distribution : The distribution of the data from ONE sample. Sampling Distribution of the Sample Mean: The distribution of the sample averages. Population Distribution 154
| | 1/6 | | | |_______________________________ Y 1 2 3 4 5 6 Shape: Center: Spread: Data Distribution - One Sample | | 1/6 | | | |_______________________________ y 1 2 3 4 5 6 Shape: Center: Spread: Sampling Distribution: Distribution of y values 155

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Shape: Look at histogram of sample means given in class Center : The mean of the sampling distribution of y equals the mean of the population. Spread : The standard deviation of y is smaller than the standard deviation of the population. Notation and Terminology: Term Pop. Sample Sampling Distn Mean µ y μ Std. Dev. σ s s n Note: The standard deviation of a statistic is called the standard error . Shape – two cases : If the population has a normal distribution, then the sampling distribution of y will have a normal distribution. Central Limit Theorem: For large n, the sampling distribution of y is approximately a normal distribution regardless of the distribution of the population . (How large is large? For this class, use n > 30) 156
In summary, it’s possible to use the normal model for quantitative and categorical situations. Ex: Consider a normal population with mean μ = 30 and standard deviation σ = 6. Suppose samples of size 4 are selected. 157 Mean (quantitative) Proportion (Categorical) Population Parameter µ p Sample Statistic sample mean, y sample proportion, ˆ p Mean of Sampling Distribution µ p Standard Error OR s n n σ (1 ) p p n - Can use bell-shaped Distribution IF Pop normal OR Data normal OR CLT: n large np >= 15 n(1-p) >= 15

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a. Find the mean and standard error of the distribution of the sample mean, y Mean Standard Error b. If a population is approximately N (30, 6), what is the probability that the average of a sample of size 4 is less than 32? c.
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## This note was uploaded on 01/10/2012 for the course MIST 3000 taught by Professor Kim during the Fall '11 term at University of Georgia Athens.

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Chapter 11 %28pages 153 -171%29 - MSIT 3000 Chapter 11...

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