Question Database: Critical Thinking
Inductive arguments (statistical generalisation)
A 1989 study reported that 65% of students in Ontario universities are moderate drinkers. The Addiction Research Foundation undertook the study. From four unidentified Ontario universities, 13, 200 full-time undergraduates were randomly selected. Questionnaires were distributed by mail. 5, 000 students responded.
1. The SAMPLE in this study is:
A. 13,200 full-time undergraduates at four Ontario universities
B. 5,000 full-time undergraduates at four Ontario universities
C. Four unidentified Ontario universities
D. All full-time undergraduates in Ontario.
2. The TARGET PROPERTY in this study is:
A. How much students drink
B. How many students there are in Ontario
C. Being an undergraduate student
D. Being a student at an Ontario university
3. The POPULATION in this study is:
A. All students at four Ontario universities.
B. All full-time undergraduate students at four Ontario universities.
C. All full-time university students in Ontario.
D. All university students in Ontario.
Answer: 1. B. 2. A. 3. D
Topic:
Inductive generalisation. Statistical inference.
Course Level:
First year, critical thinking.
Notes:
I dealt four cards from a standard, shuffled pack. 75% of them were red cards.
How reliable is this sample size of four?Suppose I kept repeating this process:
A. Shuffle the pack, deal out four cards, count the number of red cards, replace the cards.
Compare this to the following process:
B. Shuffle the pack, deal out eight cards, count the number of red cards, replace the cards.
Would I get the (atpyical) result of 75% red cards more often using process A or B?
Answer: A
Topic:
Inductive generalisation. Statistical inference.
Course Level:
First year, critical thinking.
Notes:
A certain town is served by two hospitals. In the larger hospital about 45 babies are born each day, and in the smaller hospital about 15 babies are born each day. As you know, about 50 percent of all babies are girls. The exact percentage of baby girls, however, varies from day to day. Sometimes it may be higher than 50 percent, sometimes lower. For a period of one year, each hospital recorded the days on which more than 60 percent of the babies born were girls.
Do you predict that:
A. The larger clinic recorded more such days.
B. The smaller clinic recorded more such days.
C. It makes no difference - the expected value is the same for both clinics.
Answer: B
Topic:
Inductive generalisation. Statistical inference.
Course Level:
First year, critical thinking.
Notes:
Suppose you have randomly sampled an English word from a text, is it more likely that it begins with the letter 'K' or that 'K' is the third letter?
A. 'K' is the first letter.
B. 'K' is the third letter.
Topic:
Inductive generalisation. Statistical inference. Availability bias.
Course Level:
First year, critical thinking.
Notes:
It is much easier to think of words that begin with 'K' than words with 'K' as the third letter. So most people say that words beginning with 'K' are more common. In fact, there are about twice as many words which have 'K' as the third letter. (like, lake, cake, bake, fake, sake, take, wake, rake ...)
About 5% of Australians have a certain disease. On some days, more than 15% of patients seen at clinic A (located in a small country town) were found to have the disease. That's three times the national average. In fact, over the last year, clinic A saw 30 such days, while clinic B (located in a large city) saw only 5. Clearly, there must be some environmental factor at work in the country town where clinic A is located, causing a higher than average rate of this disease.
Which of the following statements is the best evaluation of the above argument:
A. The data strongly supports the conclusion. The difference between the two clinics indicates that there is a higher incidence of the disease in the country town and environmental factors could explain this.
B. The data provides weak support for the conclusion. The difference between the two clinics points to a higher than average incidence of this disease in the country town. However, without further information, we cannot conclude that this is due to environmental factors.
C. The data provide no support for the conclusion. The difference between the two clinics does not support the conclusion that there is a higher rate of the disease in the country town. It could be due to chance alone.
D. The data do not support the conclusion. The difference between the two clinics could be explained by unreliable testing procedures used by doctors working at clinic A.
Answer: C
Topic:
Inductive generalisation. Statistical inference.
Course Level:
First year, critical thinking.