Task Sets: Making Inferences and Justifying Conclusions - Common Core Math - HS Statistics and Probability

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Foundations of Inference

A news site runs an online poll where 80,000 readers choose to click
and vote. A polling firm instead randomly selects 600 voters and
interviews them. Which sample should be trusted more, and why?

The 80,000-reader poll, because a larger sample is always more
representative.

The random sample of 600, because random selection removes
systematic bias even though it is smaller.

The 80,000-reader poll, because more responses reduce both bias
and variability.

Neither, because sample size and selection method do not affect
trustworthiness.

Three honest random samples from the same population give
$\hat{p} = 0.62$ , $\hat{p} = 0.68$ , and $\hat{p} = 0.65$ . What does
this show about the population proportion $p$ ?

The population proportion changed between the three samples.

One of the three samples must have been taken incorrectly.

$p$ is a single fixed number; each $\hat{p}$ is an estimate that
varies from sample to sample.

The population proportion is exactly $0.65$ , the middle value.

A simulation of a fair coin (200 trials of 10 flips) shows that 9 or
10 heads in 10 flips happens occasionally. A friend flips a real coin
and gets 9 heads in 10 flips. What is the correct conclusion?

The coin is proven to be unfair.

This is mild evidence to question the fair-coin model, but not
proof that the coin is unfair.

The coin is proven to be fair, since the result appeared in the
simulation.

Nothing can be said, because simulations are unreliable.

Study Design

A study draws 200 subjects at random from a city, then uses a coin
flip to place each into a treatment or control group. Which kind of
conclusion does each form of randomness make possible?

Random selection lets results generalize to the city; random
assignment lets a difference be attributed to the treatment.

Both forms of randomness do the same job, so either one alone is
enough for any conclusion.

Random selection establishes cause and effect; random assignment
lets results generalize.

Neither form of randomness affects what conclusions are
justified.

An observational study finds that students who drink coffee score
higher on exams. No one was randomly assigned to drink coffee. What
can be concluded?

Drinking coffee causes higher exam scores.

Coffee drinking is associated with higher scores, but a
confounder (such as study habits) could explain both.

Coffee drinking has no relationship to exam scores.

Higher exam scores cause students to drink coffee.

A drug is tested by randomly assigning treatment and control groups,
but the 200 subjects were unpaid volunteers, not randomly selected.
The treatment group does significantly better. What is justified?

The drug works for the volunteers studied, but the result may not
generalize to the whole population.

The drug works for everyone in the population, because the study
was randomized.

Nothing can be concluded, because volunteers were used.

The result generalizes to the population but does not show the
drug caused the improvement.

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HSS.IC Tutor Intake - Sampling, Study Design, and Statistical Inference

Foundations of Inference

Study Design