Exam 2: Reasoning With Data

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:

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?

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?

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?

Which is not a primary component in deductive reasoning?

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?

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?

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:

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

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?

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?

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

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

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?

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:

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?

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

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?

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

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