Chapter 7
Data for Decisions
Population vs Sample
•A Population in a statistical study is theentire group of individuals about which wewant information.
•A Sample is part of the population fromwhich we actually collect information usedto draw conclusions about the whole.
Sampling
•Convenience Sampling is when youselect the members of the population thatare easiest to reach. This often producesunrepresentative data.
•A sample of mall shoppers is an exampleof convenience sampling. Why would thismeans of sampling not represent thepopulation?
•The design of a statistical study is biasedif it systematically favors certain outcomes.
•A Voluntary Response Sample consistsof people who choose themselves byresponding to a general appeal. Voluntaryresponse samples are biased becausepeople with strong opinions are most likelyto respond.
•A Simple Random Sample (SRS) of size nconsists of n individuals from the populationchosen in such a way that every set of nindividuals has an equal chance to be thesample actually selected.
•Undercoverage occurs when some groups inthe population are left out of the process ofchoosing the sample.
•Nonresponse occurs when an individualchosen for the sample can’t be contacted orrefuses to participate.
Experiments
•An Observational study, such as a samplesurvey, observes individuals and measuresvariables of interest but does not attempt toinfluence the responses. The purpose of anobservational study is to describe some group orsituation.
•An Experiment, on the other hand, deliberatelyimposes some treatment on individuals in orderto observe their responses. The purpose of anexperiment is to study whether the treatmentcauses a change in the response.
•Variables, whether part of a study or not,are said to be confounded when theireffects on the outcome cannot bedistinguished from each other.
•An observed effect so large that it wouldrarely occur by chance is calledstatistically significant.
Parameters vs Statistics
•A Parameter is a number that describes thePopulation. A parameter is a fixed number, butin practice we do not know its value.
•A Statistic is a number that describes a sample.The value of a statistic is known when we havetaken a sample, but it can change from sampleto sample. We often us a statistic to estimate anunknown parameter.
Sampling Distribution
•A Sampling Distribution of a statistic is the distribution ofvalues taken by the statistic in all possible samples ofthe same size from the same population.
•Shape: For large sample sizes, the samplingdistribution of is approximately normal.
•Center: The mean of the sampling distribution is p.
•Spread: The standard deviation of the samplingdistribution is
Confidence Interval
•A 95% confidence interval is an interval obtainedfrom the sample data by a method that 95% ofall samples will produce an interval containingthe true population parameter.
•Choose a SRS of size n from a large populationthat contains an unknown proportion p ofsuccesses. A 95% confidence interval for p is
