Free Practice Quiz Question List

4 Probability and Statistical Reasoning Online Quiz Questions

Use this free practice quiz with 20 questions to review 4 Probability and Statistical Reasoning, test your knowledge, and prepare for your next test or exam.

20 questions

True or false

1 point

A fair coin has a 0.5 chance of landing heads on each toss. This means that every two tosses will contain exactly one head.

A
True
B
False

Fill in the blank

1 point

In Bayes’ rule, the prior probability of event $A$ is represented by .

Written response

1 point

A person judges an event as common mainly because examples of it come readily to mind. What heuristic is this?

Written response

1 point

What is the term for the chance difference between a sample statistic and the population parameter?

Choose one

1 point

What does the conditional probability $P(A \mid B)$ mean?

A
$P(A \mid B)$ means the probability of $B$ given $A$ .
B
$P(A \mid B)$ means the probability of $A$ given $B$ .
C
$P(A \mid B)$ means the probability that both $A$ and $B$ occur.
D
$P(A \mid B)$ means the probability of $A$ or $B$ occurring.

Fill in the blank

1 point

A numerical measure that describes a population is called a .

Choose one

1 point

A poll about all city residents is posted on a website, and 20,000 visitors choose to respond. What is the main risk to generalizing its results to the city population?

A
Sampling variability, because all samples differ from their populations by chance
B
Sampling bias, because the selection process may systematically overrepresent some groups
C
Regression to the mean, because website visitors may change their opinions
D
Conditional probability, because respondents answer a poll question

Choose one

1 point

A person estimates that someone is likely to belong to a rare occupation because that person fits a familiar stereotype, without considering how uncommon the occupation is. Which reasoning shortcut is most directly illustrated?

A
Availability, because the person’s occupation is easy to recall
B
Small-sample overconfidence, because one person is being studied
C
Representativeness, because resemblance is used while the base rate is neglected
D
Regression to the mean, because the person’s traits are unusually extreme

Choose all

1 point

Which statements about small samples are supported? Select all that apply.

A
A few observations can show greater random fluctuation than a larger sample.
B
Treating a few observations as reliably representative can be small-sample overconfidence.
C
A small sample is necessarily biased, regardless of how it was selected.
D
A sample becomes free of bias as soon as it includes more than a few observations.

True or false

1 point

If a measurement is unusually extreme, regression to the mean guarantees that the same individual's next measurement will be less extreme.

A
True
B
False

Choose one

1 point

In a population of 10,000 people, 1% have a condition. A test detects 90% of people with the condition and gives a positive result to 5% of people without it. About what percentage of positive results are true positives?

A
About 5%
B
About 15%
C
About 90%
D
About 95%

Choose all

1 point

A research team wants to use a survey sample to draw conclusions about a wider population. Which checks are important? Select all that apply.

A
Determine how participants were selected.
B
Consider who did not respond.
C
Assume a large sample is representative even if selection was voluntary.
D
Check whether the conclusion is limited to a population the sample can reasonably represent.

Choose one

1 point

Under which conditions is regression to the mean most likely to matter?

A
Cases are selected at random, and repeated measurements are identical.
B
Cases are selected because their first measurement is extreme, and follow-up measurements are imperfectly related to it.
C
Cases are selected because their first measurement is average, and follow-up measurements are unrelated to it.
D
A large sample is used, regardless of how cases were selected or measured.

Open ended

1 point

A school offers help only to students who earned exceptionally low scores on an exam. Their scores rise on a later exam. Explain why this rise alone does not establish that the help caused improvement, and describe a suitable way to assess the help’s effect.

Choose one

1 point

After seeing several dramatic news stories about house fires, Maya concludes that house fires are more common than other household emergencies, without checking population data. Which heuristic best describes her reasoning?

A
Representativeness
B
Availability
C
Regression to the mean
D
Sampling variability

Choose one

1 point

A researcher calculates the average commute time for the 120 people in a survey. What is the term for this numerical summary of the sample?

A
A population
B
A parameter
C
A statistic
D
A probability sample

Choose one

1 point

A city estimates residents’ views using a poll that invites anyone visiting its website to respond. Which conclusion about the poll is most justified?

A
The poll must be representative because many people responded.
B
The poll may not represent the target population because participation was voluntary and limited to website visitors.
C
The poll has no sampling variability because it includes many responses.
D
The poll is equivalent to a simple random sample if respondents answer honestly.

Written response

1 point

In a group of 10,000 people, 90 of the 585 people who test positive actually have the condition. What percentage of positive results are true positives? Give the nearest whole-number percentage.

True or false

1 point

A research team divides a city into neighborhoods and uses a random method to select residents from each neighborhood. This is an example of stratified sampling. True or false?

A
True
B
False

Written response

1 point

To compare competing possibilities, you rewrite percentages as counts out of a group of people, such as 1,000 or 10,000. What is this way of expressing the information called?

4 Probability and Statistical Reasoning Online Quiz Questions

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