Exam 15: Understanding Uncertainty Through Simulation

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When rolling five dice, the possible totals range from 5 (5 ones) to 30 (5 sixes).Describe how you might use a random number generator to construct a probability distribution for the outcomes of rolling five dice.

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Question 1

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Use a random number generator to uniformly generate integers from 1 to 6, in batches of 5 integers per batch.run the simulation a large number of times and then plot the relative frequency distribution of the batch totals.

Which of the following is true of computer simulations?

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In a simple game of chance, the numbers 1, 2, 3, 4, and 5 are each written on a piece of paper and placed into a hat.A player draws a piece at random, and if the player draws the "3", the player "wins".Describe how you would use simulation to estimate the probability of winning the game 2 or more times out of three plays.(Assume all numbers are returned to the hat prior to each round.)

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Question 3

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Configure a random number generator to uniformly generate random integers from 1 to 5.A "trial" consists of generating a batch of 3 random numbers.a positive result occurs when there are 2 or more "3"s in a trial.Conduct n trials, where n is large, and count the number k of positive outcomes.The approximate probability of winning 2 or more out of 3 plays is k / n.

The gas mileages (in miles per gallon, mpg) and weights (in pounds) were recorded for six makes of cars.The values had a correlation of -0.542, indicating that gas mileage decreases with increasing car weight.Describe how you would use a randomization test to estimate a p-value for the correlation value.

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Question 4

A study investigates the proportions of male and female adults who have experienced at least one headache in the past two weeks.The results are summarized below: The null hypothesis is that the proportion of persons who have experienced a headache within the past two weeks is the same for both males and females. In a simulation to estimate the p-value of the study's chi-square statistic, what value should be used for the probability that a random subject has experienced a headache within the past two weeks?

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Question 5

For a computer simulation, a frequency plot of the outcomes is called a ________________________ distribution.

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Question 6

A randomization distribution resulting from the simulation of a chi-square test had 4% of the values at or above the chi-square statistic observed for the real sample.What decision would you make for the test, using a level of 0.05?

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Question 7

If you simulate a situation n times and the outcome of interest occurs k of those times, then the probability of that outcome is approximately ______________________.(Your answer should be an algebraic formula.)

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Question 8

Describe how to estimate the p-value of a chi-square statistic using computer simulation.

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Question 9

Under what circumstances might it be useful to conduct statistical computer simulations?

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Question 10

Randomization tests are also called _____________________ tests.

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Question 11

______________________ uses computer models to mimic what might happen in the real world.

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Question 12

To simulate a situation, you need a computer or calculator that generates ______________ numbers.

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Question 13

Showing 1 - 13 of 13

When rolling five dice, the possible totals range from 5 (5 ones) to 30 (5 sixes).Describe how you might use a random number generator to construct a probability distribution for the outcomes of rolling five dice.

Which of the following is true of computer simulations?

For a computer simulation, a frequency plot of the outcomes is called a ________________________ distribution.

A randomization distribution resulting from the simulation of a chi-square test had 4% of the values at or above the chi-square statistic observed for the real sample.What decision would you make for the test, using a level of 0.05?

If you simulate a situation n times and the outcome of interest occurs k of those times, then the probability of that outcome is approximately ______________________.(Your answer should be an algebraic formula.)

Describe how to estimate the p-value of a chi-square statistic using computer simulation.

Under what circumstances might it be useful to conduct statistical computer simulations?

Randomization tests are also called _____________________ tests.

______________________ uses computer models to mimic what might happen in the real world.

To simulate a situation, you need a computer or calculator that generates ______________ numbers.

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

Psychological Influences on Personal Probability

When Intuition Differs From Relative Frequency

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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