7.1 Sampling Error The Need for Sampling Distributions
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1 7.1 Sampling Error The Need for Sampling Distributions Tom Lewis Fall Term 2009 Tom Lewis () 7.1 Sampling Error The Need for Sampling Distributions Fall Term / 5
2 Outline 1 Tom Lewis () 7.1 Sampling Error The Need for Sampling Distributions Fall Term / 5
3 A small example Five students were randomly selected from my Mathematics 140 class. Here are there scores on the first test: 47, 94, 88, 62, 64. Treat this as a population, and find its mean µ. We will estimate µ through sampling. Tom Lewis () 7.1 Sampling Error The Need for Sampling Distributions Fall Term / 5
4 A small example Five students were randomly selected from my Mathematics 140 class. Here are there scores on the first test: 47, 94, 88, 62, 64. Treat this as a population, and find its mean µ. We will estimate µ through sampling. Find the sample mean for all samples of size 1. Tom Lewis () 7.1 Sampling Error The Need for Sampling Distributions Fall Term / 5
5 A small example Five students were randomly selected from my Mathematics 140 class. Here are there scores on the first test: 47, 94, 88, 62, 64. Treat this as a population, and find its mean µ. We will estimate µ through sampling. Find the sample mean for all samples of size 1. Find the sample mean for all samples of size 2. Tom Lewis () 7.1 Sampling Error The Need for Sampling Distributions Fall Term / 5
6 A small example Five students were randomly selected from my Mathematics 140 class. Here are there scores on the first test: 47, 94, 88, 62, 64. Treat this as a population, and find its mean µ. We will estimate µ through sampling. Find the sample mean for all samples of size 1. Find the sample mean for all samples of size 2. Find the sample mean for all samples of size 3. Tom Lewis () 7.1 Sampling Error The Need for Sampling Distributions Fall Term / 5
7 A small example Five students were randomly selected from my Mathematics 140 class. Here are there scores on the first test: 47, 94, 88, 62, 64. Treat this as a population, and find its mean µ. We will estimate µ through sampling. Find the sample mean for all samples of size 1. Find the sample mean for all samples of size 2. Find the sample mean for all samples of size 3. Find the sample mean for all samples of size 4. Tom Lewis () 7.1 Sampling Error The Need for Sampling Distributions Fall Term / 5
8 A small example Five students were randomly selected from my Mathematics 140 class. Here are there scores on the first test: 47, 94, 88, 62, 64. Treat this as a population, and find its mean µ. We will estimate µ through sampling. Find the sample mean for all samples of size 1. Find the sample mean for all samples of size 2. Find the sample mean for all samples of size 3. Find the sample mean for all samples of size 4. Find the sample mean for all samples of size 5. Tom Lewis () 7.1 Sampling Error The Need for Sampling Distributions Fall Term / 5
9 Sampling from a larger population The data set was generated from sampling a normal distribution with mean µ and standard deviation σ. Tom Lewis () 7.1 Sampling Error The Need for Sampling Distributions Fall Term / 5
10 Sampling from a larger population The data set was generated from sampling a normal distribution with mean µ and standard deviation σ. First find the mean of the first 10 observations next to your name. Make a dot plot of the sample means. Tom Lewis () 7.1 Sampling Error The Need for Sampling Distributions Fall Term / 5
11 Sampling from a larger population The data set was generated from sampling a normal distribution with mean µ and standard deviation σ. First find the mean of the first 10 observations next to your name. Make a dot plot of the sample means. Second find the mean of the first 20 observations next to your name. Make a dot plot of the sample means. Tom Lewis () 7.1 Sampling Error The Need for Sampling Distributions Fall Term / 5
12 Sampling from a larger population The data set was generated from sampling a normal distribution with mean µ and standard deviation σ. First find the mean of the first 10 observations next to your name. Make a dot plot of the sample means. Second find the mean of the first 20 observations next to your name. Make a dot plot of the sample means. Compare the dot plots? Tom Lewis () 7.1 Sampling Error The Need for Sampling Distributions Fall Term / 5
13 Definition For a variable x and a given sample size, the distribution of the variable x is called the sampling distribution of the sample mean. Tom Lewis () 7.1 Sampling Error The Need for Sampling Distributions Fall Term / 5
14 Definition For a variable x and a given sample size, the distribution of the variable x is called the sampling distribution of the sample mean. Sample Size and Sampling Error The larger the sample size, the smaller the sampling error tends to be in estimating a population mean, µ, by the sample mean, x. Tom Lewis () 7.1 Sampling Error The Need for Sampling Distributions Fall Term / 5
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