Deck 15: Understanding Uncertainty Through Simulation

Question 1

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.)

Answer 1

k / n

Question 2

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

Answer 2

When computing probability distributions by hand is difficult or costly.

Question 3

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.

Answer 3

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.

Question 4

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.)

Question 5

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?

A)Do not reject the null hypothesis.There is not enough evidence to conclude that the observed chi-square value is unusual.
B)Reject the null hypothesis.There is sufficient evidence to conclude that the chi-square value is unusual.
C)Since 4% = 0.04 < 0.05, the simulation needs to include more trails.
D)There is not enough information to render a decision about the test.

Question 6

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

Question 7

Which of the following is true of computer simulations?

A)The results are only as good as the instructions and models provided to the computer.
B)Simulations are usually much more time-consuming and costly than experiments or studies.
C)Since simulations are performed by computer, human error is eliminated, and thus the simulation results describe the modeled system exactly.
D)a and c only

Question 8

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.

Question 9

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

Question 10

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?

A)0.87
B)0.16
C)0.11
D)0.13

Question 11

Randomization tests are also called _____________________ tests.

Question 12

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

Question 13

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