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Exam 16: Bootstrap Methods and Permutation Tests

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Question 1

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Residents of large urban cities often complain about the lack of parking and overpriced parking tickets.The mayor of Washington,DC,is doing a study to find out the 25% trimmed mean of all parking tickets received by residents in 1 year.A sample of 50 residents yielded a 25% trimmed mean of $150.00 and the bootstrap standard error is $23.00.What is the distribution of the critical value used to computer a 95% confidence interval?

A) t(25)
B) t(49)
C) N(0,1)
D) None of the above

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Question 2

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Bootstrapping is useful because it adds more values to the original data set.

A) True.You are able to add as many new values as needed to the original data set.
B) True.You are able to add a finite amount of new values to the original data set.
C) False.No new values are added to the data set.
D) False.Bootstrapping is only used to change the mean of the original data set.

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Question 3

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Variation in bootstrap distributions is largely based on _______.

Consider the following two statements. I: The bootstrap t confidence interval and bootstrap percentile confidence interval will agree closely when the bias of the bootstrap distribution is small. II: The bootstrap t confidence interval and bootstrap percentile confidence interval will agree closely when the bootstrap distribution is close to Normal. Which of these statements is TRUE?

Residents of large urban cities often complain about the lack of parking and overpriced parking tickets.The mayor of Washington,DC,is doing a study to find out the 25% trimmed mean of all parking tickets received by residents in 1 year.A sample of 50 residents yielded a 25% trimmed mean of $150.00 and the bootstrap standard error is $23.00.A 95% bootstrap confidence interval will be accurate only if what condition is met?

A consumer advocate is comparing income for a wide variety of jobs between the South and the Northeast.The average income of a simple random sample of 800 jobs in the Northeast is compared to the average income of a simple random sample of 750 jobs in the South.From the collected data,950 resamples are taken.Each time,750 incomes are selected with replacement from the data collected from the South,and 800 incomes are selected with replacement from the data collected from the Northeast.The distribution of the difference in means based on the resamples is shown below (in thousands of dollars) . Based on the graph,which of the following 95% bootstrap intervals is best to use to estimate the difference in mean income?

The Q-Q plot below shows the bootstrap distribution of a trimmed mean with a large bias and a large original sample.What method should be used to generate a 95% bootstrap confidence interval?

A random sample of size 25 was selected from a population and from that sample the value of a statistic,which we will label ,was determined to be = 6.250.Using the bootstrap method,5000 resamples were obtained from the sample observations.The histogram of the values of the statistic from these 5000 resamples looked reasonably Normal.The 5000 's had a mean of 6.234 and standard deviation of 1.493.An approximate 95% confidence interval for the parameter that corresponds to is given by

Give an example of the plug-in principle.

A large simple random sample is selected from a certain population and the statistic of interest is calculated.Suppose we bootstrap this statistic and wish to compute the 95% BCa confidence interval.We obtain the following computer output. BCa Confidence Intervals: 2.5% 5% 95% 97.5% Statistic 0.0253 0.0568 0.391 0.431 What is the 95% BCa confidence interval?

Bootstrap distribution based on small samples will generate bootstrap confidence intervals that are _____________.

Suppose we are interested in the amount of time (in minutes) college students spend on Facebook per day.A simple random sample of size five is taken and we obtain the numbers 120,25,365,22,and 154.Which of the following is a possible resample for bootstrapping?

In which of the following situations can we use a permutation test?

The mayor of Beltsville has commissioned a research company to estimate the average age of the houses in a large historical district in the town.Data on 120 randomly selected properties are collected,and a histogram of the sample data shows a right-skewed distribution with several large outliers.The person leading this project decides that the standard t procedures should not be used.He decides to use the 25% trimmed mean as a measure of center.The leader of the project then decides to bootstrap the 25% trimmed mean.The bootstrap distribution is shown below.Some summary measures are given as well. Number of Replications: 500 Summary Statistics: Observed Mean Bias SE TrimMean 53.675 53.05 4.67 Percentiles: 2.5% 5% 25% 50% 75% 95% 97.5% TrimMean 41.05 44.28 50.45 53.20 56.05 60.80 63.82 The dashed line in the histogram represents the mean of the resamples.The solid line represents the observed value of the trimmed mean in the original sample. As part of the summary measure,the value 4.67 is reported as the SE.How was this value calculated,and what does it represent?

A simple random sample of corporate executives is taken and their annual salaries recorded.The goal is to estimate the 25% trimmed mean of the annual salaries of the population of all corporate executives.To do this,we bootstrap the 25% trimmed mean using our sample and obtain the bootstrap distribution. Suppose we sampled 1500 corporate executives.Summary statistics are given below. What is the bootstrap,t,95% confidence interval for the 25% population trimmed mean?

The following random sample was obtained from a population with unknown mean and standard deviation. From the sample the following statistics were calculated: = 10 and s = 3.16. This sample was used to form the bootstrap distribution of the sample standard deviation based on 1000 resamples.Which of the following statements with respect to this bootstrapping process and distribution is/are FALSE?

The Q-Q plot below shows the bootstrap distribution of a trimmed mean with a small bias and a large original sample.What method should be used to generate a 95% bootstrap confidence interval?

Which of the following statements about the bootstrapping method is/are FALSE?

A simple random sample of size four is selected from a certain population.The sample yields the following data. 1 8 4 3 Suppose we bootstrap the mean of these data by drawing 1000 resamples.Suppose we find that the mean of the bootstrap distribution is 4.01.What is the bootstrap estimate of the bias of the statistic?

A large simple random sample is selected from a certain population and the statistic of interest is calculated.Suppose we bootstrap this statistic and obtain the following bootstrap distribution. Which of the following 95% bootstrap intervals is best to use?