08­03­18 Sampling and Surveys.notebook

Aug 2­4:00 PM

august 3, 2018

summary from yesterday!

What do you think would have happened if we had time to do the same activity but with a sample size of 10?

Increasing the sample size decreases the variability of the sampling distribution.

What does one of the blue dots represent?A sample of 5 words, and an average calculated from that sample.

08­03­18 Sampling and Surveys.notebook

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What is the difference between a population and a sample?

Population ­ _________________________________________________________

Sample ­ _____________________________________________________________

Parameter ­ __________________________________________________________

Statistic ­ _____________________________________________________________

the entire group of individuals under the study

part of the population actually examined in order to gather information

a number that describes some characteristic of the population(the value of the parameter is usually unknown because we cannot examine the entire population.)

a number that describes some characteristic of a sample(we use a statistic to estimate an unknown parameter)

08­03­18 Sampling and Surveys.notebook

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ways to collect data1. Census ­ _________________________________________________________________________

2.    Sampling ­ _______________________________________________________________________

attempt to contact every individual in the entire population

study a part to gain information about the whole

EXAMPLE: The student government at a high school surveys 100 of the students at the school to get their opinions about a change to the bell schedule. Identify the population and sample.

The population is all the students at school.The sample is the 100 students surveyed.

08­03­18 Sampling and Surveys.notebook

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BIAS ‐ systematically favors certain outcomes

1. _________________________

2.   ________________________________________________________________________

people choose

interviewers choosepersonal choice always produces bias(gender, race, age, religion)

Badly Designed Sampling Methods

1. Voluntary response ­ ___________________________________________________________________________________________

Ex. ________________________________________________________________________________

2. Convenience sampling ­ _________________________________________________________________________________________

people who choose themselves by responding to a general appeal. * people with strong opionions are most likely to respond. * some also allow volunteers to respond more than once!

internet survey, opinion polls, call in TV shows (American Idol)

chooses individuals easiest to reach

**AP EXAM TIP: If you’re asked to describe how the design of a study leads to bias, you’re expected to identify the direction of the bias – i.e. the method leads to an overestimate or underestimate of the population proportion.

EXAMPLE:  To estimate the proportion of families that oppose budget cuts to the athletic department, the principal surveys families as they enter the football stadium on Friday night.  Explain how this plan will result in bias and how the bias will affect the estimated proportion.

This design is biased since it systematically favors a "no" outcome. If the principal were to conduct a similar survey over and over again, each time the result will probability overestimate the proportion of people who would respond "no."

08­03­18 Sampling and Surveys.notebook

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Check your UnderstandingFor each situation, identify the sampling method used.  Then explain how the sampling method could lead to bias.

1.  A farmer brings a juice company several crates of oranges each week.  A company inspector looks at 10 oranges from the top of each crate before deciding whether to buy all the oranges.

2.  The ABC program Nightline once asked whether the United Nations should continue to have its headquarters in the United States.  Viewers were invited to call one telephone number to respond “Yes” and another phone for “No.”  There was a charge for calling either number.  More than 186,000 callers responded, and 67% said “No.”

  

Convenience sampling. This could lead him to think that the oranges are of better quality than they really are, if the farmer puts the best oranges on top!

Voluntary Response Sampling. Only those who feel particularly strongly about the issue are likely to respond. In this case, those who are happy that the United Nations has its headquarters in the United States already have what they want and so are less leikely to worry about responding to the question.

08­03­18 Sampling and Surveys.notebook

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Sampling Methods(We will do more sampling methods on Monday!)

1. Simple Random Sample (SRS): n individuals from the population are chosen in such a way that every set of n individuals has an equal chance to be in the sample actually selected.

Ways to choose a SRS:  • Drawing names of the whole population from a hat• Random Number Generator on the Calculator• Table of Random Digits

08­03­18 Sampling and Surveys.notebook

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Table of Random Digits

EXAMPLE:  Mall HoursThe management company of a local mall plans to survey a random sample of 3 stores to determine the hours they would like to stay open during the holiday season.  Use Table D at line 101 to select an SRS of size 3 stores. 

Describe your method that you used and then identify the stores that have been chosen.

08­03­18 Sampling and Surveys.notebook

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HOMEWORKpage 226 (1, 3, 7, 8, 9, 11, 13, 17)