Question 1

Suppose you hypothesized that the mean of X is 7. You then collect a sample of observations of X. Using statistical theory, you know that, if the mean of X is 7, the probability that your sample average is above 9 or below 5 is 0.05. If you observe a sample mean of 10:

Accepted Answer

A)  You make the inductive argument that the probability that your sample average is above 9 or below 5 is not 0.05. The strength of this argument is 5%. 
B)  You make the deductive argument that the probability that your sample average is above 9 or below 5 is not 0.05. The strength of this argument is 95%. 
C)  You make the inductive argument that the probability that your sample average is above 9 or below 5 is 0.05. The strength of this argument is 95%. 
D)  None of the answers is correct.

Question 2

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  48 approximately 5% of the time.
5) You observe X = 53 and conclude that the probability that X  48 is not 5%.
6) Because the probability that 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?

Accepted Answer

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

Question 3

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?

Accepted Answer

A)  Proof by induction 
B)  Proof by transposition 
C)  Direct proof 
D)  Inductive reasoning

Question 4

Suppose a fellow consultant claims that regional markets with more grocery stores per capita will be more competitive. If you assume this claim to be true, what is an empirically testable conclusion that would follow from this assumption?

Accepted Answer

A)  Grocery store sales will be higher in locations with more grocery stores per capita. 
B)  Grocery store costs of goods will be higher in locations with more grocery stores per capita. 
C)  Grocery store sales will be lower in locations with more grocery stores per capita. 
D)  Grocery store prices will be higher in locations with more grocery stores per capita.

Question 5

Which is not a primary component in deductive reasoning?

Accepted Answer

A)  Assumptions 
B)  Methods of proof 
C)  Sample of observations 
D)  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?

Accepted Answer

A)  Proof by induction 
B)  Proof by transposition 
C)  Direct proof 
D)  Inductive reasoning

Question 7

Believing that all investment funds consistently beat the market because the hedge funds that exist this year all of have beaten the market over the last decade suffers from faulty inductive reasoning because of what type of bias?

Accepted Answer

A)  Predictable-world bias 
B)  Availability bias 
C)  Over-optimism bias 
D)  Confirmation bias

Question 8

Suppose you hypothesized that the average salary in the company is $75,000. You then collect a sample of salaries for employees of the company. Using statistical theory, you know that, if the average salary is $75,000, then the probability that your sample average is above $90,000 or below $60,000 is 0.05. If you observe an average salary of $91,000:

Accepted Answer

A)  you make the inductive argument that the probability that your sample average is above $90,000 or below $60,000 is not 0.05. The strength of this argument is 5%. 
B)  you make the deductive argument that the probability that your sample average is above $90,000 or below $60,000 is not 0.05. The strength of this argument is 95%. 
C)  you make the inductive argument that the average salary in the company is not $75,000. The strength of this argument is 95%. 
D)  None of the answers is correct.

Question 9

Which of the following is an example of flawed inductive reasoning due to availability bias?

Accepted Answer

A)  Basing your assessment of the risk of a plane crash on television news reports. 
B)  Believing the odds to be in your favor at a casino after winning the lottery. 
C)  Determining the popularity of a government policy based on the opinions of your friends. 
D)  Basing your assessment of the risk of a plane crash on television news reports and determining the popularity of a government policy based on the opinions of your friends.

Question 10

Your boss claims that customers who call to complain will drop your firm's services within the next year. He provides evidence that he believes supports his claim by showing everyone who dropped your firm's service last year also complained. How should you respond?

Accepted Answer

A)  Agree that the evidence supports the claim - it suggests a proof by transposition. 
B)  Agree that the evidence supports the claim - it suggests a direct proof. 
C)  Disagree that the evidence supports the claim - it suggests a different causal relationship. 
D)  None of the answers is correct.

Question 11

Suppose a colleague claims that if the price elasticity of demand for the company's good is inelastic, then raising the price of the good will lead to higher sales. This is example of what type of reasoning?

Accepted Answer

A)  Inductive reasoning 
B)  Indirect causal relationship 
C)  Deductive reasoning 
D)  Proof by transposition

Question 12

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

Accepted Answer

A)  causal relationships. 
B)  business analytics. 
C)  predictive analytics. 
D)  reasoning.

Question 13

When making a claim via inductive reasoning, which of the following is true concerning the degree of support?

Accepted Answer

A)  A subjective degree of support has a statistical foundation, generally constructed via deductive reasoning. 
B)  A subjective degree of support has a statistical foundation, generally constructed via inductive reasoning. 
C)  An objective degree of support has a statistical foundation, generally constructed via deductive reasoning. 
D)  An objective degree of support has a statistical foundation, generally constructed via inductive reasoning.

Question 14

A poker player refuses to bet on hands with a pair of aces after losing four consecutive hands with a pair of aces. What is wrong with this logic?

Accepted Answer

A)  Predictable-world bias 
B)  Selection bias 
C)  Over-optimism bias 
D)  Confirmation bias

Question 15

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:

Accepted Answer

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.

Question 16

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  48 approximately 5% of the time.
5) You observe X = 53 and conclude that the probability that X  48 is not 5%.
6) Because the probability that 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 inductive reasoning?

Accepted Answer

A)  Step 4 only 
B)  Steps 5 and 6 only 
C)  Steps 1, 2, and 3 only 
D)  Step 5 only

Question 17

Which of the following is not a reason for weak inductive arguments?

Accepted Answer

A)  Availability bias 
B)  Statistical bias 
C)  Confirmation bias 
D)  Predictable-world bias

Question 18

After using deductive reasoning, you determine that if the probability of team A beating team B is 50% then the probability of team A beating team B four times in a row is about 6%. If after observing team A beating team B four times in a row you decide to reject the assumption that team A's likelihood of beating team B is 50%, what is the degree of support for this conclusion?

Accepted Answer

A)  6% 
B)  3% 
C)  94% 
D)  50%

Question 19

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

Accepted Answer

A)  Direct proof 
B)  Proof by induction 
C)  Proof by transposition 
D)  None of the answers is correct.

Question 20

The primary distinction between a subjective degree of support and an objective degree of support is the use of a(n):

Accepted Answer

A)  causal relationship. 
B)  statistical foundation. 
C)  empirically testable conclusion. 
D)  direct proof.

Exam 2: Reasoning With Data