Question 1

What is the common situation in which we would use simulation methods to analyze our data?

Accepted Answer

A)  For normally distributed data values 
B)  For small sample sizes 
C)  When the data violates the assumptions of all the standard tests 
D)  When the estimated population parameter differs greatly from the sample statistic 
A)  For normally distributed data values 
B)  For small sample sizes 
C)  When the data violates the assumptions of all the standard tests 
D)  When the estimated population parameter differs greatly from the sample statistic C

Question 2

Consider the two data sets shown. Imagine that we are interested if the mean of the second population is larger than the mean of the first population and we wish to test this using the bootstrap procedure. We will use a one-tailed approach with the alternative hypothesis being a situation in which the mean of the second population exceeds the first.
​
 $\begin{array}{c}
{\text { Samples }} \
\begin{array}{|ll|}
\hline 
A & \text { B } \
 5 & 9 \
6 & 8 \
8 & 7 \
4 & 5 \
7 & 9 \
3 & 8 \
9 & 5 \
1 & 5 \
5 & 7 \
2 & 8 \
\hline
\end{array}\end{array}$ 
a.Calculate the difference in means between the two data sets. Is this consistent with the null hypothesis or the alternative hypothesis?
b.Perform a single bootstrap and calculate the difference between the means of the two groups. Use the first set of digits from π below as a method to generate the appropriate random numbers for each group (treat zeroes as a 10) and then sequentially choose the appropriate number of bootstrap values from each sample, starting with the first sample. Clearly show which values you use and how (i.e., show your work).
c.Is the difference in means from part (b) consistent with the null or alternative hypothesis?
d.What would our conclusion be if we performed 99 more replicates and they showed the same general pattern (i.e., the sign of the difference) as in part (c)?
π = 31415926535897932384626433

Accepted Answer

a. The difference in means between the two data sets is:
Mean of A = (5+6+8+4+7+3+9+1+5+2)/10 = 5.0
Mean of B = (9+8+7+5+9+8+5+5+7+8)/10 = 7.1
Difference = 7.1 - 5.0 = 2.1

This is consistent with the alternative hypothesis, as the mean of the second population (B) is larger than the mean of the first population (A).

b. Using the first set of digits from π, we have:
A: 3, 1, 4, 1, 5, 9, 2, 6, 5, 3
B: 5, 8, 9, 7, 9, 3, 2, 8, 4, 6

Bootstrap sample:
A: 3, 1, 4, 1, 5, 9, 2, 6, 5, 3
B: 5, 8, 9, 7, 9, 3, 2, 8, 4, 6

Mean of A = (3+1+4+1+5+9+2+6+5+3)/10 = 4.0
Mean of B = (5+8+9+7+9+3+2+8+4+6)/10 = 6.1
Difference = 6.1 - 4.0 = 2.1

c. The difference in means from part (b) is consistent with the alternative hypothesis, as the mean of the second population (B) is still larger than the mean of the first population (A).

d. If 99 more replicates showed the same general pattern as in part (c), consistently showing that the mean of the second population is larger than the mean of the first population, then we would conclude that there is strong evidence to support the alternative hypothesis that the mean of the second population exceeds the first.

Question 3

When doing a simulation, after you assume the null hypothesis is true, what is the key value that you calculate over and over?

Accepted Answer

A)  The probability of getting the original sample statistic 
B)  The probability of getting the original test statistic 
C)  The value of the sample statistic 
D)  The value of the test statistic 
A)  The probability of getting the original sample statistic 
B)  The probability of getting the original test statistic 
C)  The value of the sample statistic 
D)  The value of the test statistic D

Question 4

To generate a bootstrap standard error of an estimate, there are four steps. Which of these is not one of them?

Accepted Answer

A)  First, use a computer to randomly sample the original data, without replacement, to make a new data set. 
B)  Second, calculate the estimate using the sampled values in the first step. 
C)  Third, repeat the first two steps a large number of times. 
D)  Fourth, the bootstrap standard error is the standard deviation of the set of values from step three. 
A)  First, use a computer to randomly sample the original data, without replacement, to make a new data set. 
B)  Second, calculate the estimate using the sampled values in the first step. 
C)  Third, repeat the first two steps a large number of times. 
D)  Fourth, the bootstrap standard error is the standard deviation of the set of values from step three.

Question 5

When we do a simulation, the distribution of test statistic values is used to calculate a P-value for our original value.

Accepted Answer

A) True 
 B)False

Question 6

The bootstrapping procedure is used to approximate which of the following distributions based on the data in the sample?

Accepted Answer

A)  Normal distribution of the mean 
B)  Poisson distribution of the median 
C)  Sampling distribution of an estimate 
D)  Distribution of values for a statistical test 
A)  Normal distribution of the mean 
B)  Poisson distribution of the median 
C)  Sampling distribution of an estimate 
D)  Distribution of values for a statistical test

Question 7

Bootstrapping is most commonly used to estimate the mean of a population.

Accepted Answer

A) True 
 B)False

Question 8

Bootstrapping can be used to calculate the standard error of almost any estimate.

Accepted Answer

A) True 
 B)False

Question 9

Consider the two data sets shown. Imagine that we are interested if the mean of the second population is larger than the mean of the first population and we wish to test this using the bootstrap procedure. We will use a one-tailed approach with the alternative hypothesis being a situation in which the mean of the second population exceeds the first.
​
 $\begin{array}{c}
{\text { Samples }} \
\begin{array}{|ll|}
\hline 
A & \text { B } \
 \hline5 & 9 \
6 & 8 \
8 & 7 \
4 & 5 \
7 & 9 \
3 & 13 \
9 & 5 \
1 & 5 \
5 & 2 \
2 & 8\
\hline
\end{array}\end{array}$ 
a.Calculate the difference in means between the two data sets. Is this consistent with the null hypothesis or the alternative hypothesis?
b.Perform a single bootstrap and calculate the difference between the means of the two groups. Use the first set of digits from π below as a method to generate the appropriate random numbers for each group (treat zeroes as a 10) and then sequentially choose the appropriate number of bootstrap values from each sample, starting with the first sample. Clearly show which values you use and how (i.e., show your work).
c.Is the difference in means from part (b) consistent with the null or alternative hypothesis?
d.What would our conclusion be if we performed 99 more replicates and they showed the same general pattern (i.e., the sign of the difference) as in part (c)?
π = 31415926535897932384626433

Accepted Answer

a. The difference in means between the t

Question 10

To generate a bootstrap standard error of an estimate, there are four steps. Which of these is not one of them?

Accepted Answer

A)  First, obtain a random sample from the original data using a computer. 
B)  Second, using the values in the first step, calculate the estimate. 
C)  Third, perform the first two steps over and over again until the cumulative value no longer changes. 
D)  Fourth, calculate the standard deviation of all the values from step three; this is the bootstrap standard error. 
A)  First, obtain a random sample from the original data using a computer. 
B)  Second, using the values in the first step, calculate the estimate. 
C)  Third, perform the first two steps over and over again until the cumulative value no longer changes. 
D)  Fourth, calculate the standard deviation of all the values from step three; this is the bootstrap standard error.

Question 11

Simulation involves sampling the original data set with replacement to create new data sets that are analyzed.

Accepted Answer

A) True 
 B)False

Question 12

To generate a bootstrap standard error of an estimate, there are four steps. Which of these is not one of them?

Accepted Answer

A)  First, obtain a random sample from the original data using a computer. 
B)  Second, using the values in the first step, calculate the variance of the estimate. 
C)  Third, perform the first and second steps over and over again. 
D)  Fourth, calculate the standard deviation of all the values from step three; this is the bootstrap standard error. 
A)  First, obtain a random sample from the original data using a computer. 
B)  Second, using the values in the first step, calculate the variance of the estimate. 
C)  Third, perform the first and second steps over and over again. 
D)  Fourth, calculate the standard deviation of all the values from step three; this is the bootstrap standard error.

Question 13

When we do a simulation, we typically sample from the population many times and calculate the test statistic each time.

Accepted Answer

A) True 
 B)False

Question 14

When deciding if we can use the bootstrapping procedure, which of the following is a requirement of our data?

Accepted Answer

A)  The sample distribution must be normal 
B)  The sample distribution must be symmetric 
C)  The sample must have a large sample size 
D)  The sample must have a small sample bias 
A)  The sample distribution must be normal 
B)  The sample distribution must be symmetric 
C)  The sample must have a large sample size 
D)  The sample must have a small sample bias

Question 15

Bootstrapping involves sampling the original population many times to create new data sets that are analyzed.

Accepted Answer

A) True 
 B)False

Question 16

When doing a simulation study, we calculate a test statistic over and over to create a distribution of values for comparison to our original test statistic value.

Accepted Answer

A) True 
 B)False

Question 17

The first step in a simulation analysis is to create a theoretical population with values matching a null hypothesis.

Accepted Answer

A) True 
 B)False

Question 18

The null distribution is best described as which of the following?

Accepted Answer

A)  The test statistic's mean value 
B)  The test statistic's distribution 
C)  The test statistic's sum of squares 
D)  The test statistic's variance 
A)  The test statistic's mean value 
B)  The test statistic's distribution 
C)  The test statistic's sum of squares 
D)  The test statistic's variance

Question 19

When performing a bootstrap, some values from the original data set may get chosen far more than others in a replicate.

Accepted Answer

A) True 
 B)False

Question 20

When doing a simulation study, if any of our test statistic values are more extreme than the original value, then we would not reject the null hypothesis.

Accepted Answer

A) True 
 B)False

What is the common situation in which we would use simulation methods to analyze our data?

When doing a simulation, after you assume the null hypothesis is true, what is the key value that you calculate over and over?

To generate a bootstrap standard error of an estimate, there are four steps. Which of these is not one of them?

When we do a simulation, the distribution of test statistic values is used to calculate a P-value for our original value.

The bootstrapping procedure is used to approximate which of the following distributions based on the data in the sample?

Bootstrapping is most commonly used to estimate the mean of a population.

Bootstrapping can be used to calculate the standard error of almost any estimate.

To generate a bootstrap standard error of an estimate, there are four steps. Which of these is not one of them?

Simulation involves sampling the original data set with replacement to create new data sets that are analyzed.

To generate a bootstrap standard error of an estimate, there are four steps. Which of these is not one of them?

When we do a simulation, we typically sample from the population many times and calculate the test statistic each time.

When deciding if we can use the bootstrapping procedure, which of the following is a requirement of our data?

Bootstrapping involves sampling the original population many times to create new data sets that are analyzed.

When doing a simulation study, we calculate a test statistic over and over to create a distribution of values for comparison to our original test statistic value.

The first step in a simulation analysis is to create a theoretical population with values matching a null hypothesis.

The null distribution is best described as which of the following?

When performing a bootstrap, some values from the original data set may get chosen far more than others in a replicate.

When doing a simulation study, if any of our test statistic values are more extreme than the original value, then we would not reject the null hypothesis.

Statistics and Samples

Displaying Data

Describing Data

Estimating With Uncertainty

Probability

Hypothesis Testing

Analyzing Proportions

Fitting Probability Models to Frequency Data

Contingency Analysis: Associations Between

The Normal Distribution

Inference for a Normal Population

Comparing Two Means

Handling Violations of Assumptions

Designing Experiments

Comparing Means of More Than Two Groups

Correlation Between Numerical Variables

Regression

Multiple Explanatory Variables

Likelihood

Meta-Analysis: Combining Information From

Filters

Exam 19: Computer-Intensive Methods

What is the common situation in which we would use simulation methods to analyze our data?

When doing a simulation, after you assume the null hypothesis is true, what is the key value that you calculate over and over?

To generate a bootstrap standard error of an estimate, there are four steps. Which of these is not one of them?

When we do a simulation, the distribution of test statistic values is used to calculate a P-value for our original value.

The bootstrapping procedure is used to approximate which of the following distributions based on the data in the sample?

Bootstrapping is most commonly used to estimate the mean of a population.

Bootstrapping can be used to calculate the standard error of almost any estimate.

To generate a bootstrap standard error of an estimate, there are four steps. Which of these is not one of them?

Simulation involves sampling the original data set with replacement to create new data sets that are analyzed.

To generate a bootstrap standard error of an estimate, there are four steps. Which of these is not one of them?

When we do a simulation, we typically sample from the population many times and calculate the test statistic each time.

When deciding if we can use the bootstrapping procedure, which of the following is a requirement of our data?

Bootstrapping involves sampling the original population many times to create new data sets that are analyzed.

When doing a simulation study, we calculate a test statistic over and over to create a distribution of values for comparison to our original test statistic value.

The first step in a simulation analysis is to create a theoretical population with values matching a null hypothesis.

The null distribution is best described as which of the following?

When performing a bootstrap, some values from the original data set may get chosen far more than others in a replicate.

When doing a simulation study, if any of our test statistic values are more extreme than the original value, then we would not reject the null hypothesis.

Statistics and Samples

Displaying Data

Describing Data

Estimating With Uncertainty

Probability

Hypothesis Testing

Analyzing Proportions

Fitting Probability Models to Frequency Data

Contingency Analysis: Associations Between

The Normal Distribution

Inference for a Normal Population

Comparing Two Means

Handling Violations of Assumptions

Designing Experiments

Comparing Means of More Than Two Groups

Correlation Between Numerical Variables

Regression

Multiple Explanatory Variables

Likelihood

Meta-Analysis: Combining Information From

Filters