Question 1

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

Accepted Answer

This description aligns with the study of decision theory and behavioral economics, which examine how individuals form beliefs based on available information and how these beliefs influence their decision-making processes under uncertainty.

Question 2

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

Accepted Answer

In a one-tailed test, the alternative hypothesis specifies a direction of the effect, indicating that the parameter of interest is either greater than or less than the null hypothesis value, hence it is an inequality.

Question 3

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

Accepted Answer

A normal distribution with a mean ($\mu$) of 0 and a standard deviation ($\sigma$) of 1 is specifically referred to as a standard normal distribution.

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 $95 \%$.

Accepted Answer

The answer of The $95 \%$ confidence interval for a...

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.

Accepted Answer

As the variance increases, the standard error increases, leading to a wider confidence interval and a smaller test statistic, which decreases the probability of rejecting the null hypothesis.

Question 6

Precision refers to the accuracy of a prediction.

Accepted Answer

The answer of Precision refers to the accuracy of a...

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.

Accepted Answer

The individual ignored the base rate probability (the overall likelihood of a taxi being blue) in favor of less reliable evidence, which is a classic example of base rate neglect.

Question 8

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

Accepted Answer

The gambler's fallacy is indeed an example of the law of small numbers, as it involves the incorrect belief that small samples of random events should reflect the overall distribution, leading individuals to expect outcomes to "even out" in the short term.

Question 9

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

Accepted Answer

This is the recency effect. The primacy effect is the opposite - it is the tendency to update one's beliefs too slowly when new information is complex.

Question 10

The availability heuristic can lead to the recency effect.

Accepted Answer

The availability heuristic, which is a mental shortcut that relies on immediate examples that come to a given person's mind when evaluating a specific topic, concept, method or decision, can indeed lead to the recency effect. The recency effect is the tendency to remember the most recently presented information best; since recent information is more readily available in memory, it can be more influential in shaping our perceptions and decisions.

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.

Accepted Answer

The campaign against smoking in the United States has utilized the availability bias by making anti-smoking ads highly visible and impactful. This strategy can lead to individuals overestimating the likelihood of death from smoking because the frequent and vivid advertisements make the consequences of smoking more mentally accessible, even if the actual statistical risk doesn't change.

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.

Accepted Answer

Heuristics are mental shortcuts or rules of thumb that simplify decision-making processes, especially in complex situations.

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) $H_{o}: \hat{p} \geq .5, ; H_{1}: \hat{p} \geq .5$.

Accepted Answer

To test whether a coin is fair, you would use a two-tailed test where the null hypothesis is that the probability of heads ($\hat{p}$) is equal to 0.5, and the alternative hypothesis is that $\hat{p}$ is not equal to 0.5. This allows for the possibility that the coin could be biased towards either heads or tails.

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) $H_{o}: \hat{p}=10 ; H_{1}: \hat{p} \neq 10$.

Accepted Answer

A two-tailed test is used when the alternative hypothesis specifies that the parameter is not equal to the stated value, which is the case in option D ($H_{o}: \hat{p}=10 ; H_{1}: \hat{p} \neq 10$). This means we are interested in deviations on both sides of the hypothesized value.

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 .

Accepted Answer

Failing to reject $H_{o}$ means that the probability of observing a result as extreme as $\hat{p}=6$ under the assumption that $p=4$ is not sufficiently low (i.e., not less than the significance level of .05). This does not provide information about the probability of observing 6 or less, the true value of $p$, or the probability of observing 6 or more being 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.

Accepted Answer

A confidence interval is the correct term for the range of values within which we believe the true value of a parameter lies, based on statistical analysis.

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.

Accepted Answer

A normal distribution is fully described by its mean and variance. The mean determines the center of the distribution, and the variance determines the spread. Other parameters like standard deviation are derived from the variance, and probability of success is not a parameter of a normal distribution.

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.

Accepted Answer

The weak law of large numbers states that as the number of observations in a sample increases, the sample average will converge in probability towards the mean of the population, but it does not guarantee that the sample average will exactly equal the population mean for any finite sample size.

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) $E(x y)=0$

Accepted Answer

If two random variables are independent, $E(x y) = E(x)E(y)$, not necessarily 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

Accepted Answer

The answer of In one week Kay predicts that it...

Quiz 7: Representativeness and Availability

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

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

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

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 $95 \%$ .

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

Precision refers to the accuracy of a prediction.

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.

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

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

The availability heuristic can lead to the recency effect.

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.

What is a heuristic?

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?

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

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?

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

A normal distribution can be fully described by which parameters.

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

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

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:

Quiz 7: Representativeness and Availability

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

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

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

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

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

Precision refers to the accuracy of a prediction.

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(P(P( taxi is blue )=.15)=.15)=.15 is called the base rate neglect.

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

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

The availability heuristic can lead to the recency effect.

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.

What is a heuristic?

I estimate that the probability of heads when tossing a coin to be p^=610\hat{p}=\frac{6}{10}p^​=106​ . Which test will I use to test whether the coin is a fair coin?

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

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

A normal distribution can be fully described by which parameters.

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

If two random variables xxx and yyy then all of the following are true except

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

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

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 $95 \%$ .

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

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.

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?

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

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: