Deck 7: Representativeness and Availability

Question 1

This chapter discusses how individuals use available information to form beliefs when facing uncertainty and how those beliefs translate into choices.

Answer 1

True

Question 2

A one-tailed test is a test in which the alternative hypothesis is an inequality.

Answer 2

True

Question 3

A normal distribution with $\mu=0$ and $\sigma=1$ is called a standard normal.

Answer 3

True

Question 4

The $95 \%$ confidence interval for a random variable with a standard normal distribution is $[1.96,-1.96]$ . Thus, that the probability of observing $\hat{\mu} \in[1.96,-1.96]$ is $95 \%$ .

Question 5

All else equal, as the variance of the random variable increases then the probability of rejecting the null at the $5 \%$ -level decreases.

Question 6

Precision refers to the accuracy of a prediction.

Question 7

In the taxi cab example, the concept that describes the mistake the individual made by identifying the taxi as blue despite the fact that $P($ taxi is blue $)=.15$ is called the base rate neglect.

Question 8

The gambler's fallacy is an example of the law of small numbers.

Question 9

The tendency to update one's beliefs too quickly when new information is easy to decipher is called the primacy effect.

Question 10

The availability heuristic can lead to the recency effect.

Question 11

In the United States, the campaign against smoking has taken advantage of individuals' availability bias. By making these ads highly visible, Americans overestimate the likelihood of death from smoking.

Question 12

What is a heuristic?

A) A mental tool employed to simplify complex decisions.
B) A bias that is observed when an individual faces complex decisions.
C) A mental tool employed to reduce the number of choices in a choice set.
D) A bias that results in an individual preferring complex decisions.

Question 13

I estimate that the probability of heads when tossing a coin to be $\hat{p}=\frac{6}{10}$ . Which test will I use to test whether the coin is a fair coin?

A) $H_{o}: \hat{p}>.5, ; H_{1}: \hat{p} \ngtr .5$ .
B) $H_{o}: \hat{p}<.5, ; H_{1}: \hat{p} \nless .5$ .
C) $H_{o}: \hat{p}=.5 ; H_{1}: \hat{p} \neq .5$ .
D) $H_{o}: \hat{p} \geq .5, ; H_{1}: \hat{p} \geq .5$ .

Question 14

Which of the following is an example of a two-tailed test?

A) $H_{o}: \hat{p}>.4, ; H_{1}: \hat{p} \ngtr .4$ .
B) $H_{o}: \hat{p}<.3, ; H_{1}: \hat{p} \nless .3$ .
C) $H_{o}: \hat{p} \geq .5, ; H_{1}: \hat{p} \geq .5$ .
D) $H_{o}: \hat{p}=10 ; H_{1}: \hat{p} \neq 10$ .

Question 15

I conduct an experiment to get an estimate of a parameter, $p$ . My estimate is $\hat{p}=6$ . Suppose I choose $\alpha=.05$ and conduct the following test: $H_{o}: \hat{p}=4 ; H_{1}: \hat{p} \neq 4$ . I fail to reject $H_{o}$ . What can I conclude?

A) The probability of observing a 6 , when $p=4$ , is greater than .05 .
B) The probability of observing 6 or less, when $p=4$ , is greater than .05 .
C) The true value of the parameter is $p=6$ .
D) The probability of observing 6 or more, when $p=4$ , is less than .05 .

Question 16

The interval on which we believe the true value of a parameter falls is called

A) A certainty interval.
B) A confidence interval.
C) An estimate interval.
D) A parameter interval.

Question 17

A normal distribution can be fully described by which parameters.

A) Mean, variance and probability of success.
B) Mean, variance and standard deviation.
C) Probability of success and variance.
D) Mean and variance.

Question 18

What is the main idea of the weak law of large numbers?

A) As the number of observations in a sample goes to infinity then the sample average converges to the mean of the population.
B) As the number of observations in a sample goes to infinity then the sample average is the mean of the population.
C) If your sample reaches some threshold number of observations, then the sample average is indistinguishable from the mean of the population.
D) It is impossible to know the average of a sample unless the mean of the population is large enough.

Question 19

If two random variables $x$ and $y$ then all of the following are true except

A) $P(x=B \mid y=A)=P(x=B)$
B) $E(x y)=E(x) E(y)$
C) $\rho(x, y)=0$
D) $E(x y)=0$

Question 20

In one week Kay predicts that it will rain with a $50 \%$ chance on Monday-Saturday and she predicts $0 \%$ chance of rain on Sunday. Kay is calibrated if it rains:

A) Monday, Sunday
B) Monday, Tuesday, Wednesday, Thursday, Friday, and Saturday
C) Monday, Wednesday, Thursday, Friday
D) Tuesday, Wednesday, Thursday

Question 21

Representativeness is:

A) A heuristic used when forming probabilistic beliefs.
B) A bias.
C) A bias that is observed when people form probabilistic beliefs.
D) A heuristic that everyone employs.

Question 22

What is the conjunction bias?

A) The belief that two events are more likely to occur than one event.
B) The belief that two events are more likely to occur together than they are alone.
C) The belief that two events are less likely to occur together than they are alone.
D) The belief that two events are correlated when they are not.

Question 23

Suppose event $A$ and event $B$ are independent. Which of the following is not true?

A) $P(A \cap B) \leq P(A)$
B) $P(A \cap B) \leq P(B)$
C) $P(A \cap B)>P(B)$
D) $P(A \cup B) \geq P(B)$

Question 24

Suppose event A and event B are independent. Which of the following is an example of the conjunction bias?

A) $P(A \cap B) \leq P(A)$
B) $P(A \cap B) \leq P(B)$
C) $P(A \cup B) \geq P(B)$
D) $P(A \cap B)>P(B)$

Question 25

I have spun the roulette wheel 5 times in a row and each time I have landed on red. Which of the following statements reflects the "law of small numbers"?

A) Since red has occurred the last 5 times, then the roulette wheel is a on a "red streak" and red will most likely occur again.
B) Since red has occurred the last 5 times, then black is "overdue" and surely the next spin will result in black.
C) The probability of red occurring is the same regardless of the last 5 spins.
D) The probability of black occurring is the same regardless of the last 5 spins.

Question 26

The tendency to not learn from newly available information is called

A) Stubbornness.
B) Law of small numbers.
C) Conservatism.
D) Representativeness.

Question 27

I am planning an event for my firm and I must choose a dinner to serve to 100 people. I decide to serve a Ceasar salad as the first course. Since I prefer anchovies on my Ceasar salad, everyone else most likely does too. So I order 100 Ceasar salads with anchovies. Which term best describes my beliefs?

A) Availability bias.
B) False Consensus.
C) Recency Effect.
D) Conservatism.

Question 28

I toss a fair coin 4 times and observe heads 3 times.
a. Using equation 7.1, what is the probability of observing 3 or fewer heads in 4 tosses of a fair coin?
b. Using equation 7.1, what is the probability of observing 3 or more heads in 4 tosses of a fair coin?
c. Write the formal test to test whether my estimate is a result of a fair coin.
d. What do you conclude?

Question 29

The state of Woolahra unrolls a new school program. Those schools that perform below the median receive additional funds for a new learning program to help the students improve and those schools that perform above the median do not receive funds for a new program. A year later the students in all schools were re-tested. Woolahra officials found that students in the low performing schools were more likely to have improved scores, whereas the students in the high performing schools were more likely to have lower scores than the previous year. The officials declared that the program was successful. What is a possible explanation for this change in scores?

Question 30

Holly has a fair coin and a 10-sided die. If the coin comes up heads, then Holly rolls the die: if a 1 or 2 is rolled Holly wins $\$ 1$ and if a 3,4,5,6,7,8,9,10 is rolled Holly win a mug. If the coin comes up tails, then Holly rolls the die: if a 1,2,3,4,5,6,7 Holly wins $\$ 1$ and a mug and if $8,9,10$ is rolled Holly only wins a mug.
A. What is the probability that Holly wins $\$ 1$ ?
B. Holly wins a mug. What is the probability that the coin came up heads?