Exam 10: Inductive Logic

Which of Mill's Methods is illustrated in the following passage? If, in your opinion, the conclusion reached indicates that an inadequate hypothesis was employed, explain why and formulate a better hypothesis. Eastlake planted sunflowers in 64 separate plots, varying soil composition with the absence or presence of six ingredients (potash, potassium, iron, etc.) with one plot for each possible combination. The sunflowers that grew invariably came in two sizes. Upon further investigation, Eastlake found that the larger plants were always in plots containing nitrate. As a result, nitrate has now become a standard ingredient in sunflower fertilizer.

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?

An argument with false premises is uncogent.

If the occurrence of X brings about Y, then

Two statements are independent when neither affects the probability of the other.

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. Over the last year, Janelle has subscribed to Mother Jones, and the Utne Reader, both of which are liberal political magazines. She has enjoyed reading most of the articles in each issue. When Janelle hears about The New Republic, a new conservative political magazine, she decides to subscribe, expecting that she will enjoy reading at least some of the articles in the coming year.

Symbols list Where necessary, you may use the list below to copy-and-paste symbols into your answer. →;↔;•;~;⋁;\;≠;$;× Suppose that you have an ordinary deck of playing cards. Assuming that you are as likely to draw one card as another, what is the probability that on your next draw you will select an ace or a king?

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(~A)

In order to be properly constructed, an argument must avoid any fallacy of incomplete evidence.

In order to be random, a sample of a population must meet the requirement that

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 jack on the first draw then drawing a queen on the second draw)

The appropriate size of a sample depends on all of the following except

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 aces on three consecutive draws)

The primary difference between inductive and deductive logic is that

In the following induction by enumeration, identify the sample and the population, and discuss the appropriateness of sample size and method of surveying. Three times Janis brought a half-gallon of water to a boil, and each time it began boiling at 212 degrees Fahrenheit. Janis concluded that this is the boiling point of water.

Which of the following is a statistical syllogism?

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 • A)

In the following induction by enumeration, identify the sample and the population, and discuss the appropriateness of sample size and method of surveying. In a recent random poll of New Jersey voters, 73 percent of the 4,622 respondents said they would vote Republican in the race for seats in the state's House of Representatives. Consequently, after the next election Republicans are sure to take the majority of available seats in the New Jersey House of Representatives.

Which of Mill's Methods is illustrated in the following passage? If, in your opinion, the conclusion reached indicates that an inadequate hypothesis was employed, explain why and formulate a better hypothesis. Benjamin observed the hibernation pattern of the small brown bear over a period of fifteen years. In the first five years the winters were unseasonably warm, with temperatures rarely dipping below freezing, and during that period of time Benjamin noticed that the bears hibernated very little. During the next five years, the winters were quite harsh (temperatures consistently below 0°) and the bears were in hibernation throughout most of the winter. Over the past five years the winters have been about average with temperatures consistently hovering in the 20s, and Benjamin has noticed that although the bears were more active than they had been the previous five years, they were not nearly as active as they had been during the first five years of the study. He concluded on the basis of these observations that there is a direct causal relationship between the winter temperatures and the length of hibernation for the small brown bear.

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((A • ~A) → B)