Take this Exam: AP Statistics — collecting data | Zestly

Question 1

In an invented study a researcher records how many hours each of a hundred students spends in the library and compares that with their final marks. The study is large, carefully conducted and carefully analysed. Why is it still an observational study rather than an experiment?

Accepted Answer

Because the researcher did not decide how long anyone would spend in the library — the students chose that for themselves, and nothing was imposed

Answer

Because no control group was set aside to be compared against the others

Answer

Because the students were not assigned to groups at random

Answer

Because a hundred students is too few for a study to count as an experiment

Question 2

An invented trial compares a new revision technique with the usual one. It assigns pupils to the two methods at random, runs both alongside each other, and uses sixty pupils in each group rather than three. What does each of those three features accomplish?

Accepted Answer

Comparison gives something to measure the new technique against; random assignment spreads unmeasured differences between pupils evenly across the groups, so a gap in outcomes is unlikely to be explained by who ended up where; and enough pupils per group makes it unlikely that a gap of that size arose by chance alone

Answer

Random assignment removes lurking variables from the study entirely, comparison controls for them a second time, and replication proves the finding is real

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Comparison shows the technique works, random assignment makes the pupils representative of all pupils, and a large group removes the need for a control

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All three exist to make the sample resemble the wider population, which is what allows the conclusion to be applied elsewhere

Question 3

In an invented trial of a hypothetical memory supplement, one group receives the supplement and the other an identical-looking pill with no active ingredient. Neither the participants nor the staff recording the results know who received which. What does that arrangement accomplish?

Accepted Answer

It removes two sources of bias: participants reporting differently because they believe they are being treated, and staff observing or recording differently because they know who is

Answer

It guarantees that the two groups are comparable at the start of the trial

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It allows the result to be applied to the population the participants came from

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It stops the placebo effect from occurring, so that only the supplement's real effect remains

Question 4

In an invented survey of towns, those with more public parks are found to sell more ice cream. A critic points out that warmer towns tend to have both. What has the critic identified?

Answer

Undercoverage, since some towns were absent from the list the sample was drawn from

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Voluntary response bias, since towns with strong views about parks would be likelier to take part

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Confounding: a third variable associated with both the explanatory and the response variable, so that the observed association has an explanation other than the one proposed

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Non-response bias, since towns that declined to supply figures may differ from those that supplied them

Question 5

In an invented study, a researcher draws fifty pupils at random from the roll of one large secondary school, then assigns each of them at random to a new teaching method or to the existing one. What may she conclude from a difference in test scores?

Answer

That the method caused the difference, and that the finding applies to secondary pupils generally

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That the method caused the difference, and that the finding applies to the pupils of that school — but to no wider population, since only that school's roll was sampled

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That the finding applies to the pupils of that school, but no causal claim is available without a larger study

Answer

That neither a causal claim nor any generalisation is available from a study of this size