Lesson test: Where intuition fails

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Where intuition fails

1.[3p]
A city of $10$ million contains $1000$ terrorists. A system flags $99$ percent of them and $1$ percent of everyone else. What is the probability that a flagged person is a terrorist? Give the answer to four decimal places.

CorrectNot quite: 0.0098

2.[3p]
What is the prosecutor's fallacy?

Treating $P (evidence ∣ innocent)$ as if it were $P (innocent ∣ evidence)$

Correct

Assuming the defendant is guilty before the trial

The answer is: Treating $P (evidence ∣ innocent)$ as if it were $P (innocent ∣ evidence)$

Using a prior that is too small

The answer is: Treating $P (evidence ∣ innocent)$ as if it were $P (innocent ∣ evidence)$

Reporting a probability without a confidence interval

The answer is: Treating $P (evidence ∣ innocent)$ as if it were $P (innocent ∣ evidence)$

3.[3p]
What was wrong with the $1$ in $73$ million figure given in the Sally Clark trial?

Select all that apply

It squared a single-death rate, treating two cot deaths in one family as independent

Correct

It answered a different question from the one the court had to decide

Correct

It was never compared with the rarity of the alternative, double murder

Correct

It used the wrong single-death rate for the population

The answer is: It squared a single-death rate, treating two cot deaths in one family as independent, It answered a different question from the one the court had to decide, It was never compared with the rarity of the alternative, double murder

4.[3p]
Why do the children of very tall parents tend to be shorter than their parents?

An extreme measurement is extreme partly through noise, and the noise is redrawn

Correct

A biological force pulls the population back towards the average

The answer is: An extreme measurement is extreme partly through noise, and the noise is redrawn

Tall parents tend to marry shorter partners

The answer is: An extreme measurement is extreme partly through noise, and the noise is redrawn

Because height is not inherited

The answer is: An extreme measurement is extreme partly through noise, and the noise is redrawn

5.[3p]
Twenty independent tests are run at the $0.05$ threshold on data with no real effect. What is the probability that at least one is significant? Give the answer to four decimal places.

CorrectNot quite: 0.6415

6.[2p]
What threshold does the Bonferroni correction use for each of $20$ tests, to keep the overall false positive rate near $0.05$ ?

CorrectNot quite: 0.0025

7.[3p]
Returning bombers were hit mostly on the wings and rarely on the engines. Where should the armour go?

The engines, since aircraft hit there did not return to be counted

Correct

The wings, since that is where the hits are

The answer is: The engines, since aircraft hit there did not return to be counted

Evenly across the aircraft

The answer is: The engines, since aircraft hit there did not return to be counted

Nowhere: the data says the aircraft are already well protected

The answer is: The engines, since aircraft hit there did not return to be counted

8.[2p]
A coincidence that would be very unlikely for any particular person is still unlikely to happen to somebody in a large population.

True

The answer is: False

False

Correct

9.[3p]
Match each failure to the quantity it drops.

Base rate neglect
Prosecutor's fallacy
Regression to the mean
Multiple comparisons
Survivorship

how common the alternatives are
the number of tests run
the noise in an extreme measure
the filter that made the sample
the direction of the conditional

Show the answer

Base rate neglect: how common the alternatives are Prosecutor's fallacy: the direction of the conditional Regression to the mean: the noise in an extreme measure Multiple comparisons: the number of tests run Survivorship: the filter that made the sample

1.[3p] A city of 10 million contains 1000 terrorists. A system flags 99 percent of them and 1 percent of everyone else. What is the probability that a flagged person is a terrorist? Give the answer to four decimal places.

2.[3p] What is the prosecutor's fallacy?

3.[3p] What was wrong with the 1 in 73 million figure given in the Sally Clark trial?

4.[3p] Why do the children of very tall parents tend to be shorter than their parents?

5.[3p] Twenty independent tests are run at the 0.05 threshold on data with no real effect. What is the probability that at least one is significant? Give the answer to four decimal places.

6.[2p] What threshold does the Bonferroni correction use for each of 20 tests, to keep the overall false positive rate near 0.05?

7.[3p] Returning bombers were hit mostly on the wings and rarely on the engines. Where should the armour go?

8.[2p] A coincidence that would be very unlikely for any particular person is still unlikely to happen to somebody in a large population.

9.[3p] Match each failure to the quantity it drops.

1.[3p]
A city of $10$ million contains $1000$ terrorists. A system flags $99$ percent of them and $1$ percent of everyone else. What is the probability that a flagged person is a terrorist? Give the answer to four decimal places.

2.[3p]
What is the prosecutor's fallacy?

3.[3p]
What was wrong with the $1$ in $73$ million figure given in the Sally Clark trial?

4.[3p]
Why do the children of very tall parents tend to be shorter than their parents?

5.[3p]
Twenty independent tests are run at the $0.05$ threshold on data with no real effect. What is the probability that at least one is significant? Give the answer to four decimal places.

6.[2p]
What threshold does the Bonferroni correction use for each of $20$ tests, to keep the overall false positive rate near $0.05$ ?

7.[3p]
Returning bombers were hit mostly on the wings and rarely on the engines. Where should the armour go?

8.[2p]
A coincidence that would be very unlikely for any particular person is still unlikely to happen to somebody in a large population.

9.[3p]
Match each failure to the quantity it drops.