AP Stats 3A, 3B, 3C

how to choose a SRS

1. assign a unique number to each member of the population from 1 - N 2. use a calculator or randomness table to select n unique numbers; don't account for repeats or unused numbers 3. subjects corresponding to the chosen numbers are in the sample

With our modern-day caller ID feature, many people do not want to answer their phone when a polling organization calls. Why might this yield a biased result in the survey about the number of computers or laptops?

People in economically disadvantaged situations are less likely to have smartphones and therefore more likely to answer a polling call. This would generate an underestimate of the number of people who own a computer or laptop.

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. What bias and in what direction is this?

This is a convenience sample, leading to bias in the fact that the oranges at the top likely have better quality than the oranges elsewhere. It creates an overestimation of the true average quality of the oranges

In 1936, the Literary Digest used the phone book to send out a presidential poll. 2.4 million out of 10 million mailed ballots were returned. 57% percent said they'd vote for Alf Landon(Rep) and 43% would say they voted for FDR. In the actual election, Landon only won electoral votes from 2 states. What bias does this demonstrate, why, and in what direction?

This is undercoverage bias because during the Great Depression, only wealthy residents wouldve been able to afford and been listed in the phone book. Economically disadvantaged people had little to no chance of being chose.

In 2016, Britain's Natural Environment Research Council used an online poll to choose the name of its new 300 million dollar ship. The winning name was "Boaty McBoat Face", which received 124,000 votes, far more than the serious candidates. What bias and in what direction is this?

This is voluntary bias, leading to an overestimate in the true percentage of people who wanted Boaty McBoat Face as a name. Since people could choose to participate, its likely that respondants were less serious about scientific pursuits than the British population as a whole

An ad for an upcoming TV show asked: should handgun control be tougher? you can call the shots, if yes, contact (), if not, contact (). Over 90% of the people who called in said yes. What is the example this is trying to make? What bias is there, in what direction?

This is voluntary response bias in the sense that those who support handgun control would be more likely to call in as they likely feel much more passsionate about it

sample

a subset of the population that actually gets examined or measured

systematic random sampling

begin with a randomly selected individual(N/n), every nth member after that will be in the sample; larger values of n egnerate smaller samples

larger random samples give _________

better information about a population

benefit of systematic random sampling

can be easier to use than a SRS, especially if the population is lined up or listed already

benefit of cluster random sampling

can make sampling less expensive by reducing travel times

A marine biologist wants to estimate the mean size of the barnacle Semibalanus balnoides on a stretch of rocky shoreline. To do so, he randomly selects twenty 10-cm square plots and measures the size of every barnacle. This is an example of:

cluster sampling

census

collect data from every member of the population

inference

drawing a conclusion about a population based on dtaa from a sample

simple random sample(SRS)

every group of n individuals in the population has an equal chance of getting selected; equivalent of throwing all members of a population into a hat, mixing it up, then drawing without replacement

nonresponse bias

happens when a portion of the chosen sample doesnt respond to the survey; the non respondants may share a common characteristic such as being stressed or busy

undercoverage bias

happens when a subgroup of the population has little or no chance of being chosen

response bias

happens when the method of the survey(or the wording) influences the response given by the subjects

voluntary response bias

happens when the sample is made up of subjects who choose themselves to participate; commonly found in online polls

what defines a good estimate?

low bias and low variability

benefits of stratified random sampling

reduces variability in the sample statistic, guarantees that all subgroups are represented in the sample

random sampling typically produces a sample that is_________

representative of the population

convenience sample

select individuals from the population who are easy to reach

cluster random sampling

split the sampling frame into heterogenous clusters/members that are in close proximity to each other, then randomly choosing several clusters; you sample ALL of the subjects within these selected clusters

stratified random sampling

split the sampling frame into homogenous groups, then pick a random sample from each group

A public opinion poll in Ohio wants to determine whether or not registered voters in the state approve of a measure to ban smoking in all public areas. They select a simple random sample of fifty registered voters from each county in the state and ask whether they approve of disapprove of the measure. This is an example of:

stratified random sample

population

the larger group that we hope to learn something about

nonresponse bias vs undercoverage bias

the sampling frame in undercoverage bias isnt complete, groups arent even included in the options; in nonresponse bias, you're still part of the group, you just don't answer

sampling variability

we don't expect the statistic from a sample to be the same as if we calculated it from the population