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Stat 110

by: Kayla Ann Berube

Stat 110 Stat 110

Marketplace > Math > Stat 110 > Stat 110
Kayla Ann Berube


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Notes for Chapters 3 and 4
Introduction to Statistical Reasoning
Wilma Sims
Class Notes
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This 3 page Class Notes was uploaded by Kayla Ann Berube on Thursday January 21, 2016. The Class Notes belongs to Stat 110 at a university taught by Wilma Sims in Spring 2016. Since its upload, it has received 8 views.


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Date Created: 01/21/16
What Do Samples Tell Us? •   Parameter o   A number that describes the population. It is a fixed number, but we usually don’t know its value. •   Statistic o   A number that describes a sample. Its value it computed from sample information, but it can change from sample to sample. Proportions •   We want to estimate the proportion of individuals in a population with a certain characteristic (“success”). •   The population proportion, p, is an unknown parameter. •   We wish to estimate p based on a sample. •   Example: o   Take a SRS of size n from a population with p successes. o   p hat is the sample proportion where… count of successes in the sample §   p hat = n Error in Estimation •   We wish to estimate a parameter from a statistic. •   Bias o   Consistent, repeated deviation of the sample statistic from the population parameter in the same direction when we take many samples. •   Variability o   Describes how spread out the values of the sample statistic are when we take many samples. •   A good sampling method has both small bias and small variability. Margin of Error •   A statistic, calculated from a random sample, will usually not estimate the parameter exactly. •   Surveys often report a percentage and a “margin of error”. •   “Margin of error or minus 3 percentage points” means that 95% of all samples would give a result within plus or minus 3 percentage points of the true parameter. •   A margin of error tells us how close our estimate comes to the truth. •   Quick method for margin of error (MOE): o   Use the sample proportion, p hat, from a SRS of size n to estimate an unknown population proportion p. o   The margin of error for 95%  confidence  is  approximately:   §   1  divided  by  the  square  root  of  n Confidence Statements •   We say we are 95% confident that the true value of the parameter lies within the margin or error. •   Confidence Statement o   Indicates how precise a statistic is by giving a degree of sureness that the actual parameter is within the range given by the statistic and its margin of error. o   p hat + MOE •   Hints for interpreting confidence statements: o   The conclusion of a confidence statement always applies to the population, not to the sample. o   Our conclusion about the population is never completely certain. o   A sample survey can choose to use a confidence level other than 95%. o   To decrease the width of a 95% confidence interval (i.e. have a samller margin of error), increase the sample size. Sample Surveys in the Real World •   Sampling and statistics seem simple, but some problems can arise. •   Sampling Errors: o   Errors caused by the act of taking a sample. They cause sample results to be different from the results of a census. •   Errors in Sampling: o   Undercoverage §   Occurs when some groups in the population are left out of the process of choosing the sample. §   Sampling Frame •   A list of all available members of the population from which the sample will be selected. o   Random Sampling Error §   Results from chance selection in the SRS. §   The error is due to chance (always present). §   A large sample helps control this. §   The margin of error includes only random sampling error. o   Nonsampling Errors §   Errors not related to the act of selecting a sample from the population. They can be present even in a census. §   Nonresponse (missing data) •   Refusal to answer survey, subject is not available for survey. §   Response Errors •   Subject may lie or remember incorrectly, subject may not understand question. §   Processing Error •   Math errors, coding data incorrectly. §   Effects of Data Collection Procedure •   Wording of the question, timing/events, how survey is administered (mail, telephone, personal interview). How to Live with Errors in Sampling •   Substitute other households for non-responders. •   Weight the responses o   Can also account for the differences by race, age, household size, etc. o   Helps correct bias, but increases variability. Stratified Random Sampling Design •   Step 1: Divide the sampling frame into groups of individuals called strata. o   The strata are chosen using some characteristic of the individuals already known and of special interest. •   Step 2: Take a separate simple random sample in each stratum and combine these to make up the stratified random sample. Probability Sample •   A sample chosen in such a way that we know what samples are possible and what chance, or probability, each possible sample has to be chosen (not all need to be equally probable). •   Simple random and stratified random are probability samples.


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