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Statistics 208 Week 7 Day 2 (Chapter 10 - Sample Surveys)

by: Katelyn Notetaker

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Statistics 208 Week 7 Day 2 (Chapter 10 - Sample Surveys) Stat 208

Marketplace > Northern Illinois University > Statistics > Stat 208 > Statistics 208 Week 7 Day 2 Chapter 10 Sample Surveys
Katelyn Notetaker
NIU
GPA 3.8

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Statistics
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Carrie Helmig
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This 3 page Class Notes was uploaded by Katelyn Notetaker on Tuesday October 4, 2016. The Class Notes belongs to Stat 208 at Northern Illinois University taught by Carrie Helmig in Fall 2016. Since its upload, it has received 6 views. For similar materials see Statistics in Statistics at Northern Illinois University.

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Date Created: 10/04/16
Sample Surveys Chapter 10  1 10.1 The Three Big Ideas of Sampling  1. We would like to know about an entire population of individuals, but examining all of  them is impractical, if not impossible.  a.  Thus we examine a smaller group of individuals called a sample selected from  the population. Hopefully the sample is representative of the population.  b.  Sample surveys are studies that ask questions of a sample drawn from some  population in the hope of learning something about the entire population. • Ex.  Opinion polls, voter preference  c. Selecting a sample to represent the population fairly is extremely difficult.  Samples that don’t represent every individual in the population fairly are said to  be biased.  d. It is almost impossible to recover from a biased sample.  2. Randomize  a. The best way to avoid a bias sample, is to use a random sample in which each  individual is given a fair, random chance of being selected for the sample.  b.  Randomization does 2 things for the sample:   i. It protects against bias.  ii. It makes it possible for us to draw inferences about the population based  on the sample.  3. It’s the Sample Size  a. Question: How large does a random sample need to be in order to be reasonably  representative of the population?  i. Answer: You might think that you need a large percentage or fraction of  the population.  ii. WRONG!! All that matters is the number of individuals in the sample.  iii. The sample size needed depends upon what you are trying to estimate.  10.2 Populations and Parameters  A population parameter is a numerically valued attribute of a model for a population. o Ex. Pop mean, µ, pop SD, σ, etc.   Statistics are values calculated from the sample.  o Ex. Sample mean, , sample SD, s   We need to be sure that the statistics we compute from the sample reflect the  corresponding parameters accurately. A sample that does this is said to be representative.  Why not take a sample that consists of the entire population, called a census? •  o Difficult to complete  o Too expensive  o Impractical – ex taste tester for beer   Populations rarely stand still  o births/deaths   Can be more complex than sampling.  o Over count individuals – college students  o  under count individuals ­ homeless  10.3 Simple Random Samples 10.4 Other Sampling Designs   A simple random sample, SRS, of size n is one in which each set of n elements in the  population has an equal chance of selection.  o To select a sample at random, we first need to define where the sample will come  from. The sampling frame is a list of individuals from which the sample is drawn. o  Samples drawn at random generally differ from one another. Each draw of  random numbers selects different people for our sample. These differences lead to different values for the variables we measure. We call these sample­to­sample  differences sampling variability.  Different Sampling Designs: T o he SRS is NOT the only fair way to draw a sample. However, all statistical  sampling designs have in common the idea that chance, not human choice, is used to select the sample.  o 1. Stratified Random Sample – a sampling design in which the population is  divided into several subpopulations, or strata, and random samples are then drawn on the stratum. If the strata are homogeneous but different from each other, a  stratified sample may yield more consistent results. • Generally used to reduce  variability.  o 2. Cluster Sampling – splitting the population into similar parts or clusters can  make sampling more practical. Then you could simply select one or a few clusters at random and perform a census within them. • Custer Sampling is generally  selected for reasons on efficiency, practicality and cost.  o 3. Multistage Sampling – a sampling scheme that combines several sampling  methods. For example, a national polling service may stratify the country by  geographical regions, select a random sample of cities from each region, then  interview.  o 4. Systematic Sampling – a sample drawn by selecting individuals systematically  from a sampling frame.   Ex. We might survey every 10th person on an alphabetical list of students. To make it random, you must start the systematic selection from a  randomly selected individual among the first 10. 5  10.7 Common Sampling Mistakes  What can go WRONG! Will go WRONG!!!   Voluntary Response Bias – bias is introduced to a sample when individuals can choose  on their own whether to participate in the sample. Samples based on voluntary response  are always invalid and cannot be recovered, no matter how large the sample is.  o Usually only those who have a strong opinion one way or another answer surveys. o Undercoverage or Use of a Bad Sampling Frame – a sampling scheme in which  some portion of the population is not sampled at all or has a smaller  representation in the sample than it has in the population.   1936 Election between Roosevelt and Landon   Convenience Sampling – a convenience sample consists of individuals  who are conveniently available – not every individual in the population is  equally convenient to sample.   Nonresponse bias – occurs when individuals choose not to answer all or part of the  survey.   Response bias refers to anything in the survey design that influences the responses.

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