Exam 10: Inductive Logic

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. A recent survey of students currently enrolled at Northern University indicated that 96 percent plan to return to the campus in the fall. Rosemary is currently enrolled at Northern University, so odds are she'll be returning to the campus in the fall, even though she has been offered a full scholarship at Oxford University.

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(B • ~B)

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. George has been having a streak of unusually bad luck. He totaled his car in a snowstorm last week, then fell on the ice and broke his leg. Two days later his wife left him, saying she was no longer willing to put up with his "little infidelities." Then just yesterday, he was fired from his job as a computer programmer because his program error rates were consistently too high and he missed too many deadlines. He began to regret ignoring his mother's advice to throw a pinch of salt over his left shoulder after he spilled that salt last month.

The sampling error is the difference between the percentage of one random sample that has an attribute and the percentage of another random sample of the same population that has that attribute.

Mill's Methods provide us with patterns of reasoning to reach general conclusions of the form "All P are Q."

Formulating and testing hypotheses involves

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 a red card and drawing a black card on two consecutive draws, in either order)

Arguments from authority may fail in all of the following ways except

The method of difference involves

In the following induction by enumeration, identify the sample and the population, and discuss the appropriateness of sample size and method of surveying. 63 percent of the 1,432 people who filled out questionnaires at Armadillo Mall in Texas are in favor of the death penalty. Consequently, 63 percent of Americans are in favor of the death penalty.

Use the rules of probability to determine the strength of the following argument. In other words, given that the premises are true, how likely is the conclusion? Even though I know the dice are not loaded or off balance, I just know that if I roll them I'll get snake eyes. I always have before.

Bayes' theorem cannot be applied if a precise numerical value cannot be assigned to the prior probability of the hypothesis.

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. By 2,025, at least 51 percent of Americans will be over the age of 65. My neighbor's great-great-granddaughter is an American, so by 2,025 she will be over the age of 65.

A sample is biased when it is not representative of a population.

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(C/D)

P(~S) = P(S) - 1.

A strong argument guarantees the truth of its conclusion.

Rejecting a scientific hypothesis is strictly a matter of applying modus tollens reasoning.

If we know that P(h/e) = 3/5, we may conclude that P(~h/e) = 2/5.

When "→" is understood as the material conditional, P(p → q) is equal to