Exam 10: Inductive Logic

P(e/h) is the probability that the hypothesis is

Applied to evidence e and hypothesis h, the conditional rule says P(h = e) =

Symbols list Where necessary, you may use the list below to copy-and-paste symbols into your answer. →;↔;•;~;⋁;\;≠;$;× Assume that P(A) = 3/5, P(B) = 3/10, P(C) = 7/10, P(D) = 4/5, and P(A/B) = 7/10. Assuming that C and D are independent, determine the following probability: P(D/C)

Identify the hypothesis in the following argument; and, if it fails to meet the four criteria for good scientific hypotheses, state which criterion is violated, and explain your answer. Jorge has been struggling to earn an A in his history class. He received a 78 percent on his first exam after studying for one whole hour. For the second exam, Jorge studied almost two hours, and earned 87 percent. For each of the last two exams, Jorge studied for one hour each day over the week before the exam and earned 97 percent and 98 percent. He realizes now that performing well on a test often requires a significant amount of study time.

Suppose you draw a card from a deck, do not replace it, then draw a second card. What rule would you use to determine the probability of drawing an ace and then drawing a black card?

Given that p and q are mutually exclusive, to determine P(p ⋁ q) we should use

Of the following, which would reduce sampling error?

P(~h/e) = 1 - P(h/e)

Symbols list Where necessary, you may use the list below to copy-and-paste symbols into your answer. →;↔;•;~;⋁;\;≠;$;× You have an ordinary deck of cards. You draw one card, do not replace it, and then draw a second card. Each series of draws begins with a full deck. Assuming you are as likely to draw one card as another, find the following probability: P(drawing hearts on first draw • drawing spades on second draw)

Indicate whether or not the following argument has the form of a statistical syllogism; and, if the argument contains information that suggests a possible fallacy of incomplete evidence, explain why. Voluntary tests of 25,000 drivers throughout the United States showed that 25 percent of them use some drug, but that 85 percent use no drugs at all while driving. The conclusion was that 15 percent of U.S. drivers do use drugs while driving. A remarkable conclusion. The tests were taken at random times of the day at randomly selected freeway restaurants.

If a sample of a population is not random, then it is biased.

In the statement "99 percent of all philosophers are wise but not wealthy," the sample is

Indicate whether or not the following argument has the form of a statistical syllogism; and, if the argument contains information that suggests a possible fallacy of incomplete evidence, explain why. On average, men with only a high school degree make only 25 percent as much money in a lifetime as men with a college degree. That means that Peter, who has a high school degree but never finished college, will only make 25 percent as much money as his brother Bill, who has both a high school and a college degree.

Analyze the following argument in terms of the schema for arguments from analogy. Briefly state at least one criticism that calls the strength of the argument into question. . . . the simplest form of the theological argument from design, once well known under the name of "Paley's watch." Paley's form of it was just this: "If we found by chance a watch or some other intricate mechanism we should infer that it had been made by someone. But all around us we do find intricate pieces of natural mechanism, and the processes of the universe are seen to move together in complex relations; we should therefore infer that these too have a Maker." (B. A. O. Williams, "Metaphysical Arguments," in The Nature of Metaphysics, D. F. Pears, ed.)

Which of the following is not a characteristic of a good sample of a population?

Analyze the following argument in terms of the schema for arguments from analogy. Briefly state at least one criticism that calls the strength of the argument into question. Nancy is thinking of buying a new car. In 1986 she bought a new Honda Civic and was very happy with it. It was a two-door hatchback with a four-cylinder engine and manual transmission (stick shift). In 1994 she bought another new two-door hatchback Honda Civic with manual transmission and a four-cylinder engine. Both cars got between 36 and 40 miles per gallon. In the market for a new car again, Nancy is planning to buy another Honda, this time a 2002 four-door Accord with automatic transmission and a six-cylinder engine, and expects to get between 36 and 40 miles per gallon in her new car.

The sampling error is defined as

In the following induction by enumeration, identify the sample and the population, and discuss the appropriateness of sample size and method of surveying. I stood at the entrance to the Business School and asked 24 Southern University students going into the building who they favored for student body president. Sixteen of the 24 said they favored Jaxson, a marketing major. So, in the campuswide election, Jaxson will get two-thirds of the vote. (Northern has a student population of 12,000).

The essential feature of a strong argument is that

The probability that I will not select a king from a well-shuffled deck of cards is