Question 1

If you are trying to prove that A causes B, why does it make sense to have your null hypothesis be "A does not cause B"?
A) Data cannot confirm a hypothesis.
B) It is easier to make strong inductive arguments when rejecting a hypothesis.
C) We must allow for B to cause A.
D) Data cannot confirm a hypothesis and it is easier to make strong inductive arguments when rejecting a hypothesis.

Accepted Answer

In scientific research, it's generally not possible to prove a hypothesis directly with data; instead, data can be used to reject a null hypothesis, leading to stronger inductive arguments. This approach allows for a more rigorous testing of the causal relationship between A and B.

Question 2

In the deductive reasoning behind the claim that "If firms can price discriminate, then prices will be higher in markets with lower price elasticities of demand" the role of "prices will be higher in markets with lower price elasticities of demand" is:
A) a method of proof.
B) a conclusion.
C) a sample.
D) an assumption.

Accepted Answer

"Prices will be higher in markets with lower price elasticities of demand" is the conclusion of the deductive reasoning. It follows from the premise that firms can price discriminate.

Question 3

Which of the following is an example of the use of Transposition as a method of proof for "If A, then B"?
A) A implies B
B) Not B implies A
C) Not A implies B
D) Not B implies Not A

Accepted Answer

Transposition is a method of proof that involves proving "If A, then B" by showing "If not B, then not A." This is exactly what choice D states, making it the correct example of the use of Transposition.

Question 4

I give you a coin, and you flip it 100 times. Let X = the number of heads observed in those 100 flips. You build the following line of reasoning: Steps 1) You assume each flip is an independent, random outcome. 2) You assume the coin is fair. 3) Using your statistics book, you conclude that X is distributed binomial with mean 50 and variance 25. 4) Based on this distribution, you conclude that you would observe X < 41 or X > 59 approximately 5% of the time. 5) You observe X = 37 and conclude that the probability that X < 41 or X > 59 is not 5%. 6) Because the probability that X < 41 or X > 59 is not 5%, you conclude the coin is not fair. Which of these steps is part of deductive reasoning? A) Steps 1, 2, 3, 4, and 6 only B) Steps 4 and 6 only C) All 6 steps D) Steps 3, 4, and 5 only

Accepted Answer

Deductive reasoning involves starting with a general statement or hypothesis and examining the possibilities to reach a specific, logical conclusion. Steps 1, 2, 3, 4, and 6 follow this pattern, starting from general assumptions about the coin and its flipping outcomes to conclude about the fairness of the coin based on observed outcomes and statistical reasoning.

Question 5

A conclusion whose validity can be meaningfully tested using observable data is an example of:
A) inductive reasoning.
B) data mining.
C) empirically testable conclusion.
D) direct proof.

Accepted Answer

An empirically testable conclusion is one that can be verified or rejected by observing and collecting relevant data. This is a crucial aspect of the scientific method and distinguishes science from other forms of reasoning or inquiry, such as deductive reasoning or speculation. Inductive reasoning involves making generalizations based on specific observations, which may or may not be supported by empirical evidence. Data mining is a process of analyzing large datasets to discover patterns or relationships, but it does not necessarily involve testing hypotheses or making empirical predictions. Direct proof is a method of demonstrating the truth of a mathematical or logical statement using logical deduction or axioms, but it may not be relevant or applicable to all types of conclusions.

Question 6

Suppose we are proving the statement that if two integers are even, then their sum is even. We execute the proof by first showing that if integer A and B are even, then they can be defined as A = 2k and B = 2m. We then note that their sum must be A + B = 2(k + m), which must be even. This is an example of what type of proof?
A) Proof by induction
B) Proof by transposition
C) Direct proof
D) Inductive reasoning

Accepted Answer

This is a direct proof because we took the given premise and directly showed that it implies the conclusion using logical reasoning.

Question 7

Given that an individual's presence at the scene of the crime is required in order for that individual to commit the crime, the use of alibis, or evidence of suspects being somewhere other than the crime scene at the time of the crime is an example of what sort of proof?
A) Proof by induction
B) Proof by transposition
C) Direct proof
D) Inductive reasoning

Accepted Answer

Proof by transposition works by showing that if a certain condition were true (in this case, the suspect committing the crime), then a specific outcome must necessarily follow (the suspect being at the crime scene). By presenting an alibi, the argument is made in reverse to show that because the specific outcome (presence at the crime scene) did not occur, the initial condition (the suspect committing the crime) must also not be true. This is a classic example of proof by transposition, also known as proof by contrapositive.

Question 8

You having two employees working on commission - employee A and employee B. Over the course of 80 weeks, you observe the sales of each employee. Let X = the number of times employee A has more sales than employee B. You build the following line of reasoning: Steps 1) You assume each sales observation is an independent, random outcome. 2) You assume each employee has equal likelihood of have greater sales in a week. 3) Using your statistics book, you conclude that X is distributed binomial with mean 40 and variance 20. 4) Based on this distribution, you conclude that you would observe X < 32 or X > 48 approximately 5% of the time. 5) You observe X = 53 and conclude that the probability that X < 32 or X > 48 is not 5%. 6) Because the probability that X < 32 or X > 48 is not 5%, you conclude employee A and employee B do not have equal likelihood of having greater sales in a week. Which of these steps is part of deductive reasoning? A) Steps 1, 2, 3, and 4 only B) Steps 1, 2, 3, 4, and 6 only C) All 6 steps D) Steps 3, 4, and 5 only

Accepted Answer

Steps 1-4 use deductive reasoning to draw a conclusion based on the assumptions and the binomial distribution. Step 6 also uses deductive reasoning to reach a conclusion based on the observed probability not matching the expected probability. Step 5, however, is based on the observation of a specific outcome and is not deductive reasoning, but rather inductive reasoning.

Question 9

Which of the following is not an empirically testable conclusion?
A) The unemployment rate would not have risen above 8% if the U.S. Treasury would have bailed out Lehman Brothers leading into the Great Recession.
B) Larger firms are more productive.
C) Multinational firms pay higher wages.
D) States with minimum wage laws experience higher unemployment rates.

Accepted Answer

The statement regarding the unemployment rate and the U.S. Treasury's actions with Lehman Brothers is not empirically testable because it is a counterfactual statement about what might have happened under different historical conditions, which cannot be directly tested or observed.

Question 10

The process of forming conclusions, judgments, or inferences from facts or premises is:
A) causal relationships.
B) business analytics.
C) predictive analytics.
D) reasoning.

Accepted Answer

The process described can be classified as reasoning. A conclusion or judgment is typically drawn based on logical reasoning from available information.

Question 11

I give you a coin, and you flip it 100 times. Let X = the number of heads observed in those 100 flips. You build the following line of reasoning: Steps 1) You assume each flip is an independent, random outcome. 2) You assume the coin is fair. 3) Using your statistics book, you conclude that X is distributed binomial with mean 50 and variance 25. 4) Based on this distribution, you conclude that you would observe X < 41 or X > 59 approximately 5% of the time. 5) You observe X = 37 and conclude that the probability that X < 41 or X > 59 is not 5%. 6) Because the probability that X < 41 or X > 59 is not 5%, you conclude the coin is not fair. Which of these steps is part of inductive reasoning? A) Step 5 only B) Steps 5 and 6 only C) Steps 1, 2, and 3 only D) Step 6 only

Accepted Answer

The answer of I give you a coin, and you...

Question 12

For the purposes of reaching sound conclusions with data analysis it is critical that:
A) data mining is used.
B) the reasoning/logic is sound.
C) causal inference is used.
D) None of the answers is correct.

Accepted Answer

While data mining can certainly be helpful in uncovering patterns and trends in large datasets, it is ultimately the reasoning and logic applied to the data that allows for sound conclusions to be reached. Causal inference can also be useful in certain contexts, but is not always necessary for reaching sound conclusions. Therefore, the best choice is B, as it is always critical to have sound reasoning and logic when conducting data analysis.

Question 13

Which is not a primary component in deductive reasoning?
A) Assumptions
B) Methods of proof
C) Sample of observations
D) Conclusions

Accepted Answer

In deductive reasoning, we start from a general principle, make assumptions, apply methods of proof to arrive at a conclusion. Sample of observations is not a primary component in deductive reasoning.

Question 14

Which method of proof is generally more effective at identifying hidden or implicit assumptions of an argument?
A) Direct proof
B) Proof by induction
C) Proof by transposition
D) None of the answers is correct.

Accepted Answer

Proof by transposition, also known as proof by contrapositive, involves examining the negation of the conclusion and proving the negation of the premise. This method forces us to consider the implicit assumptions of the argument and identify any hidden premises that may be necessary for the argument to hold. As a result, proof by transposition can be more effective at identifying hidden or implicit assumptions than direct proof or proof by induction.

Question 15

A description of the rules and/or steps behind the reasoning process is known as:
A) logic.
B) business analytics.
C) predictive analytics.
D) causal relationships.

Accepted Answer

The description of rules and steps behind the reasoning process is the definition of logic. Business analytics is a term used to describe the collection, analysis, and interpretation of business data. Predictive analytics involves using statistical methods to forecast future outcomes. Causal relationships focus on identifying cause-and-effect relationships between variables.

Question 16

In the deductive reasoning behind the claim that "If firms sell homogenous products, then prices should fall to marginal costs" the role of "firms sell homogenous products" is:
A) a method of proof.
B) a conclusion.
C) the sample.
D) an assumption.

Accepted Answer

"Firms sell homogenous products" is an assumption because it is a premise that must be true in order for the claim to hold. It is not a conclusion that can be deduced from other premises, nor is it a method of proof or a sample.

Question 17

By showing your colleague that the conclusions of your analysis regarding the optimal pricing strategy for the firm would be the same under a variety of different assumptions regarding the price response of competitors is an example of:
A) direct proof.
B) selection bias.
C) robustness.
D) degree of support.

Accepted Answer

The scenario described is an example of robustness, which refers to the ability of a conclusion to hold true even under different assumptions or scenarios. By showing that the optimal pricing strategy remains the same under various assumptions about competitor response, the analysis demonstrates that the conclusion is robust and not dependent on a specific set of assumptions.

Question 18

To prove the claim that "If an individual's income goes up, their demand for our product goes up" by Transposition it would suffice to show:
A) any individual with falling demand must have falling income.
B) every individual with increasing income has increasing demand.
C) any individual with falling income has falling demand.
D) None of the answers is correct.

Accepted Answer

Transposition involves proving the contrapositive. The contrapositive of "If income goes up, demand goes up" is "If demand does not go up, income does not go up," which is equivalent to "If demand falls, income falls."

Question 19

Which of the following are empirically testable conclusions?
A) The average price of cable television will be higher if DirecTV and Comcast are allowed to merge relative to if they are not.
B) Price markups should be lower in markets with more firms.
C) Your career earnings will be higher if you get an MBA.
D) None of the answers is correct.

Accepted Answer

The answer of Which of the following are empirically testable...

Question 20

If you are intending to refute conclusions drawn via clear deductive reasoning, what must you disagree with?
A) The assumptions
B) The methods of proof
C) The assumptions and the methods of proof
D) The assumptions or the methods of proof

Accepted Answer

To refute conclusions drawn via clear deductive reasoning, you must disagree with either the assumptions or the methods of proof used in the argument. Disagreeing with both the assumptions and methods of proof would also work as it falls within the scope of disagreeing with either one of them.

Quiz 2: Reasoning With Data

If you are trying to prove that A causes B, why does it make sense to have your null hypothesis be "A does not cause B"?

In the deductive reasoning behind the claim that "If firms can price discriminate, then prices will be higher in markets with lower price elasticities of demand" the role of "prices will be higher in markets with lower price elasticities of demand" is:

Which of the following is an example of the use of Transposition as a method of proof for "If A, then B"?

A conclusion whose validity can be meaningfully tested using observable data is an example of:

Given that an individual's presence at the scene of the crime is required in order for that individual to commit the crime, the use of alibis, or evidence of suspects being somewhere other than the crime scene at the time of the crime is an example of what sort of proof?

Which of the following is not an empirically testable conclusion?

The process of forming conclusions, judgments, or inferences from facts or premises is:

For the purposes of reaching sound conclusions with data analysis it is critical that:

Which is not a primary component in deductive reasoning?

Which method of proof is generally more effective at identifying hidden or implicit assumptions of an argument?

A description of the rules and/or steps behind the reasoning process is known as:

In the deductive reasoning behind the claim that "If firms sell homogenous products, then prices should fall to marginal costs" the role of "firms sell homogenous products" is:

By showing your colleague that the conclusions of your analysis regarding the optimal pricing strategy for the firm would be the same under a variety of different assumptions regarding the price response of competitors is an example of:

To prove the claim that "If an individual's income goes up, their demand for our product goes up" by Transposition it would suffice to show:

Which of the following are empirically testable conclusions?

If you are intending to refute conclusions drawn via clear deductive reasoning, what must you disagree with?