In chapter 12 of the text, we learned that a generalization is reasonable only if it is based upon a large enough sample, where “large enough” is defined by the underlying variability of the population, the desired level of confidence, and the stated margin of error. And it also requires that the sample be random (or stratified). In regards to polling people, we added that the questions must be well-framed (i.e., not loaded, overly broad, or ambiguous) and the responds free to answer.
For each of the following generalizations, determine whether it is prima facie (on the face of it, i.e., without reading any other information to what is stated) reasonable and why, or prima facie unreasonable (i.e. fallacious) and why.
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Question 1 of 10
This poll of 1,600 MIT students shows that they work 60 hours a week. This is proof that college students are working long hours doing their college work.
Question 2 of 10
I went to the Grand Opening of that new restaurant Thornton’s Bar and Grill, and the food was not very good. You can bet I won’t be going back.
Question 3 of 10
Both my friends use DermaSchmeer anti-acne cream, and they don’t even suffer from acne outbreaks. That’s why I’ve ordered the cream for myself.
Question 4 of 10
Researchers hand-raised four unrelated crow chicks in separate cages full of twigs. At between two and two-and-a-half months, all the checks spontaneously started using twigs to try to locate food. It is probable then, that most crows are born with the ability quickly develop the ability to use twigs to locate food.
Question 5 of 10
In a survey of 1,600 American homes called by a random digit dialer during the hours of 7am and 11pm, 62% of the respondents said they intended to vote to re-elect President Smith for a second term. The pollsters conclude that if the election were held today, Smith would win with 62% plus or minus 3% of the vote.
Question 6 of 10
In a survey of 1,600 American homes called by a random digit dialer between 9am and 5pm, 55% say they are happy with the current tax system. The pollsters conclude that about 55% plus or minus 3% of Americans support the current tax system.
Question 7 of 10
American researchers conduct a randomized poll of 1,600 people in California and New York, and find that 80% say that America is not a better county than France. They conclude that Americans do not feel that their country is superior to France.
Question 8 of 10
Psychologists interview 100 randomly chosen Americans and find out that 87% of them love dogs. So they psychologists conclude that more than ¾ of all Americans love dogs.
Question 9 of 10
Psychiatrist to friend: “Most of my patients are troubled teenagers. So don’t tell me teenagers today aren’t troubled!”
Question 10 of 10
A survey is conducted by French researchers. They personally interview a stratified random sample of 2,500 Americans, and 60% of the sample says that France is more culturally advanced than America. So they conclude that between 58% and 62% of Americans believe France is more culturally advanced than America.