Exam 17: When Intuition Differs From Relative Frequency

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Explain how a misinterpretation of a coincidence could impact a town that is experiencing an unusually high rate of cancer, compared to the rest of the country.

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Question 1

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People may automatically think there is something wrong with the water, soil, air, or a variety of things, and start to panic, sue companies, get media attention, or pressure the government to get involved, all without proper substantiation of an actual problem.Any Rare event is going to happen to someone, somewhere, sometime.

A(n) __________ is a surprising concurrence of events, perceived as meaningfully related, with no apparent causal connection.

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Question 2

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coincidence

What can happen when a physical situation lends itself to computing a relative-frequency probability, but people ignore that information and go with their 'intuition'?

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this can lead to incorrect thinking and to incorrect probabilities, or to incorrect interpretation of probabilities.

If the bookmakers who run sports betting operations were to set fair odds, so that both the house and those placing bets had expected values of zero, then the probabilities for all of the players should sum to 1, but they don't.Do they sum to a higher or lower value, and why?

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Question 4

Explain what it means for a test result to be a false positive.

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Question 5

What is meant by the 'specificity' of a test for a certain disease?

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Question 6

Which of the following describes the 'specificity' of a test for a certain disease?

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Question 7

Do you agree with the following statement regarding sequences of tosses of a fair coin? Explain why or why not."The sequence HHHHTH doesn't represent the fairness of the coin, and therefore is not as likely to occur as sequences such as HTHTTH."

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Question 8

The probability of a coincidence happening may be __________ than you think.

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Question 9

Suppose a lottery game has a 1/1000 chance of winning for each ticket, and the prize is $1,000.How much should you be willing to pay for a ticket in order to have a positive expected value?

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Question 10

What is meant by a test result that is a false positive?

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Question 11

In which of the following situations would the gambler's fallacy not apply?

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Question 12

Which of the following lottery combinations (6 numbers from 1-30, no repeats allowed) is the least likely to come up as a winning ticket?

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Question 13

About how many people would need to be gathered together to be at least 50% sure that two of them will share the same birthday (the same day of the year, not necessarily the same year)?

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Question 14

Research shows that people tend to "detect" patterns even where none exist, and to __________ the degree of clustering of outcomes in sports events, as in other sequential data (for example the chance of being on a shooting streak in basketball).

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Question 15

What is meant by the 'sensitivity' of a test for a certain disease?

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Question 16

Which of the following beliefs are examples of the gambler's fallacy?

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Question 17

In what sense is a coincidence not an improbable event?

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Question 18

Which of the following sequences of six tosses of a fair coin is more likely (if either): HTHTTH, or HHHTTT? Explain your answer.

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Question 19

Which of the following coincidences reflects a truly improbable event, if interpreted properly?

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Question 20

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Exam 17: When Intuition Differs From Relative Frequency

Explain how a misinterpretation of a coincidence could impact a town that is experiencing an unusually high rate of cancer, compared to the rest of the country.

A(n) __________ is a surprising concurrence of events, perceived as meaningfully related, with no apparent causal connection.

What can happen when a physical situation lends itself to computing a relative-frequency probability, but people ignore that information and go with their 'intuition'?

If the bookmakers who run sports betting operations were to set fair odds, so that both the house and those placing bets had expected values of zero, then the probabilities for all of the players should sum to 1, but they don't.Do they sum to a higher or lower value, and why?

Explain what it means for a test result to be a false positive.

What is meant by the 'specificity' of a test for a certain disease?

Which of the following describes the 'specificity' of a test for a certain disease?

Do you agree with the following statement regarding sequences of tosses of a fair coin? Explain why or why not."The sequence HHHHTH doesn't represent the fairness of the coin, and therefore is not as likely to occur as sequences such as HTHTTH."

The probability of a coincidence happening may be __________ than you think.

Suppose a lottery game has a 1/1000 chance of winning for each ticket, and the prize is $1,000.How much should you be willing to pay for a ticket in order to have a positive expected value?

What is meant by a test result that is a false positive?

In which of the following situations would the gambler's fallacy not apply?

Which of the following lottery combinations (6 numbers from 1-30, no repeats allowed) is the least likely to come up as a winning ticket?

About how many people would need to be gathered together to be at least 50% sure that two of them will share the same birthday (the same day of the year, not necessarily the same year)?

Research shows that people tend to "detect" patterns even where none exist, and to __________ the degree of clustering of outcomes in sports events, as in other sequential data (for example the chance of being on a shooting streak in basketball).

What is meant by the 'sensitivity' of a test for a certain disease?

Which of the following beliefs are examples of the gambler's fallacy?

In what sense is a coincidence not an improbable event?

Which of the following sequences of six tosses of a fair coin is more likely (if either): HTHTTH, or HHHTTT? Explain your answer.

Which of the following coincidences reflects a truly improbable event, if interpreted properly?

The Benefits and Risks of Using Statistics

Reading the News

Measurements, Mistakes, and Misunderstandings

How to Get a Good Sample

Experiments and Observational Studies

Getting the Big Picture

Summarizing and Displaying Measurement Data

Bell-Shaped Curves and Other Shapes

Plots, Graphs, and Pictures

Relationships Between Measurement Variables

Relationships Can Be Deceiving

Relationships Between Categorical Variables

Statistical Significance for 2 2 Tables

Understanding Probability and Long-Term Expectations

Understanding Uncertainty Through Simulation

Psychological Influences on Personal Probability

Understanding the Economic News

The Diversity of Samples From the Same Population

Estimating Proportions With Confidence

The Role of Confidence Intervals in Research

Rejecting Chancetesting Hypotheses in Research

Hypothesis Testingexamples and Case Studies

Significance, Importance, and Undetected Differences

Meta-Analysis: Resolving Inconsistencies Across Studies

Ethics in Statistical Studies

Putting What You Have Learned to the Test

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