The Ideas of Statistics — Module Assessment

Question 1

What two historical activities are usually described as the early roots of statistics?

Accepted Answer

State record-keeping and games of chance

Answer

Astronomy and medicine

Answer

Biology and economics

Answer

Philosophy and law

Question 2

What is Adolphe Quetelet best known for contributing in the nineteenth century?

Accepted Answer

The idea of the average man and applying the normal distribution to human traits

Answer

The first modern significance test

Answer

The correlation coefficient named after him

Answer

The law of large numbers

Question 3

In the cookie example (Bowl 1: 30 vanilla, 10 chocolate; Bowl 2: 20 vanilla, 20 chocolate), you draw a vanilla cookie. What is the probability it came from Bowl 1?

Accepted Answer

60 percent

Answer

50 percent

Answer

75 percent

Answer

40 percent

Question 4

Which statement best captures the difference between the frequentist and Bayesian schools?

Accepted Answer

Frequentists treat probability as long-run frequency, while Bayesians treat it as a degree of belief updated with evidence.

Answer

Frequentists use data while Bayesians ignore it.

Answer

Bayesians never use any prior information.

Answer

The two schools are identical in every practical situation.

Question 5

Which design starts with healthy people and follows them forward in time to see who develops a disease?

Accepted Answer

A cohort study

Answer

A case-control study

Answer

A cross-sectional survey

Answer

A meta-analysis

Question 6

Why did the apparent heart benefit of hormone replacement therapy largely disappear when tested in a randomized trial?

Accepted Answer

Confounders like wealth and health-consciousness had inflated the benefit in observational data

Answer

The randomized trial used far fewer participants

Answer

Observational studies had measured heart attacks incorrectly

Answer

The therapy changed formulation between the studies

Question 7

Why is random assignment considered the strongest way to establish a causal effect?

Accepted Answer

It balances both measured and unmeasured confounders across the groups

Answer

It guarantees the two groups have exactly equal outcomes

Answer

It eliminates the need for a control group

Answer

It always uses a larger sample than observational studies

Question 8

What best describes a natural experiment?

Accepted Answer

A situation where nature, policy, or history assigns groups in a nearly random way that a researcher can exploit

Answer

An experiment conducted outdoors in a natural setting

Answer

Any observational study with a very large sample

Answer

A trial in which participants choose their own group

Question 9

A study reports p = 0.02. Which statement is correct?

Accepted Answer

If there were truly no effect, data this extreme would be fairly unlikely.

Answer

There is a 98% chance the effect is real.

Answer

The result is guaranteed to replicate.

Answer

The effect must be large and important.

Question 10

What is 'p-hacking'?

Accepted Answer

Trying many analyses and reporting only the one that reaches significance.

Answer

Stealing data from other researchers.

Answer

A special statistical test designed for very large datasets.

Answer

Pre-registering a hypothesis before collecting any data.

Question 11

In Breiman's 'Two Cultures', what defines the algorithmic-modeling culture?

Accepted Answer

Using algorithms such as random forests chosen mainly for predictive accuracy, treating the mechanism as unknown.

Answer

Assuming the data come from a known stochastic model and estimating its parameters.

Answer

Refusing to use computers or software of any kind.

Answer

Relying only on data visualisation rather than models.

Question 12

Why do machine-learning practitioners evaluate models on a held-out test set?

Accepted Answer

To guard against overfitting by measuring error on data the model has not seen.

Answer

To increase the size of the training sample.

Answer

Because journals require it for publication.

Answer

To force the model to become as simple as possible.

Question 13

A test is described as "95 percent accurate" for a condition that affects 1 in 1,000 people. Someone tests positive. What does the statistical mind conclude?

Accepted Answer

Because the condition is rare, most positives are false alarms, so the chance of real disease is still low.

Answer

The positive result is almost certainly correct, because 95 percent is a high accuracy.

Answer

The test is useless and should be ignored entirely.

Answer

Accuracy figures cannot be reasoned about without the exact formula.

Question 14

Which statement best captures how a statistical mind treats uncertainty?

Accepted Answer

It quantifies the uncertainty, decides within it, and stays ready to update as evidence arrives.

Answer

It answers every question with caveats and avoids committing to any decision.

Answer

It seeks a single confident number so the uncertainty disappears.

Answer

It trusts intuition over data because the numbers are always uncertain anyway.