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

The observation of a sample mean of 10, when the hypothesis suggests a mean of 7 with a 5% probability of the sample mean being above 9 or below 5, does not directly allow for the calculation of the strength of an argument as described in options A, B, or C. The observation suggests that the hypothesis might be incorrect, but it does not directly translate into the probabilities or argument strengths as described in the options.

Question 2

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

Given the observed average salary of $91,000, which falls outside the expected range if the true average were $75,000 (with a 5% probability of such an extreme result occurring by chance), you can inductively argue that the true average salary is likely not $75,000. The strength of this argument corresponds to the confidence level, which is 1 - 0.05 = 95%.

Question 3

Reasoning that goes from the general to the specific or "top-down" logic is known as:

Accepted Answer

Deductive reasoning is a logical process in which a conclusion is reached by starting with a general principle or premise and applying it to a specific case. This is also known as "top-down" logic because it starts with a broad or general idea and then narrows down to a specific conclusion. Inductive reasoning, on the other hand, involves using specific observations or evidence to draw a general conclusion. Proof by transposition and direct proof are specific types of deductive reasoning and do not encompass the broader concept of "top-down" logic.

Question 4

I give you a die, and you roll it 600 times. Let X = the number of ones observed in those 600 rolls. You build the following line of reasoning: Steps 1) You assume each roll is an independent, random outcome. 2) You assume the dice is fair. 3) Using your statistics book, you conclude that X is distributed binomial with mean 100 and variance 83. 4) Based on this distribution, you conclude that you would observe X < 82 or X > 118 approximately 5% of the time. 5) You observe X = 123 and conclude that the probability that X < 82 or X > 118 is not 5%. 6) Because the probability that X < 82 or X > 118 is not 5%, you conclude the die is not fair. Which of these steps is part of inductive reasoning?

Accepted Answer

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

Question 5

Suppose a salesperson claims Brand A is more effective at cleaning dishes than Brand B. If you assume this claim to be true, what is an empirically testable conclusion that would follow from this assumption?

Accepted Answer

If we assume that Brand A is more effective at cleaning dishes than Brand B, an empirically testable conclusion that would follow from this assumption is that the probability a dish gets cleaned using Brand A is higher than the probability it gets cleaned using Brand B. This could be tested by conducting a controlled experiment where dishes are washed with both brands and the success rate of cleaning is measured and compared between the two brands. The other answer choices are not necessarily true based on the assumption given.

Question 6

Why is it that inductive reasoning does not involve a proof?

Accepted Answer

Inductive reasoning involves making generalizations based on specific observations or experiences. While these generalizations may be supported by evidence, they cannot be proven with certainty as there may be exceptions or counterexamples. Therefore, inductive reasoning does not involve a proof in the same way that deductive reasoning does.

Question 7

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

Accepted Answer

The answer of When making a claim via inductive reasoning,...

Question 8

The primary difference between the population and a particular data sample is that:

Accepted Answer

The population is the entire group that we are interested in studying, while a data sample is a subset of that population. This means that the sample is not the entire universe of potential observations, but rather a smaller subset of it. The other answer choices may be characteristics of a good sample, but they do not explain the primary difference between a population and a sample.

Question 9

Which of the following conclusions is an example of inductive reasoning?

Accepted Answer

This conclusion is based on specific evidence from one region and is being applied to a broader population, making it an example of inductive reasoning.

Question 10

A business analyst uses data mining to establish a negative correlation between customer complaints and customer relations training hours for employees. She concludes increasing training will reduce customer complaints. What is a key weakness in this approach as stated?

Accepted Answer

The weakness in this approach is that the strength of the inductive reasoning used to establish the negative correlation is unknown. Therefore, it is possible that there may be other factors affecting the relationship between customer complaints and customer relations training hours that were not taken into account.

Question 11

Reasoning that goes from the specific (e.g., a data sample) to the general (e.g. the population) is known as:

Accepted Answer

Inductive reasoning involves using specific observations or data to make generalizations or hypotheses about a larger population. Deductive reasoning, on the other hand, involves applying general principles or theories to specific situations or observations. Proof by transposition and direct proof are specific methods of mathematical proof and are not related to the question at hand.

Question 12

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

If there is more competition, then prices should be lower.

Question 13

Degrees of support based off opinion and ultimately lacking any statistical foundation are often termed:

Accepted Answer

Degrees of support based off opinion and lacking statistical foundation are subjective, meaning they are based on personal feelings and beliefs rather than objective facts.

Question 14

Which of the following conclusions is an example of deductive reasoning?

Accepted Answer

Choice C is an example of deductive reasoning, because it presents a logical statement about the relationship between industry supply and quantity supplied based on a known economic concept. The other choices may be based on observations or trends, but they do not necessarily follow a logical deductive thought process. Additionally, choice D is an example of faulty deductive reasoning, as it relies on a limited sample size to draw a broad conclusion.

Question 15

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

Accepted Answer

An objective degree of support relies on a statistical foundation, which is based on empirical data and can be tested and verified objectively. In contrast, a subjective degree of support is based on personal opinion or belief and lacks a statistical or empirical foundation. Therefore, the use of a statistical foundation is the primary distinction between the two.

Question 16

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

The fact that team A beat team B four times in a row with a probability of 6% under the assumption that team A has a 50% chance of winning supports the conclusion that team A's actual probability of winning is different from 50%. Since the probability of team A winning four times in a row is small under the assumption of a 50% probability of winning, observing this result indicates that the assumption is unlikely to be true. Therefore, there is a high degree of support (94%) for rejecting the assumption that team A's likelihood of beating team B is 50%.

Question 17

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

The evidence provided only shows a correlation between customers who complained and those who dropped the service, but it does not prove that complaining caused them to drop the service. There could be other factors at play, such as poor customer service or dissatisfaction with the service itself. Therefore, it would be a mistake to assume a causal relationship between complaining and dropping the service without further evidence.

Question 18

Taking samples of registered voters and asking them to disclose their preferences leading up to elections in order to assess the view of all registered voters on a particular candidate is an example of what sort of reasoning?

Accepted Answer

This is an example of inductive reasoning because it involves making generalizations based on specific observations or samples. In this case, the generalization is about the preferences of all registered voters based on the preferences of a sample of voters.

Question 19

The statement, "The Golden State Warriors are the most watched basketball team in the Oakland TV market, therefore they are the most watched NBA team" is an example of what type of reasoning?

Accepted Answer

This is an example of inductive reasoning, where a general conclusion is drawn from specific observations or examples. The statement provides a specific example (Golden State Warriors being the most watched team in the Oakland TV market) and then draws a broader conclusion (they are the most watched NBA team). However, this conclusion may not be true for other TV markets outside of Oakland.

Question 20

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 inductive reasoning?

Accepted Answer

Step 5 is inductive reasoning because it involves drawing a conclusion based on a specific observation (X = 53) rather than on general principles or laws.

Quiz 2: Reasoning With Data