Exam 16: Bootstrap Methods and Permutation Tests

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). The mean of the resamples is $7393,and the standard deviation of the resamples is $10,807.What is the value of the bootstrap standard error?

What is the main advantage of using a permutation test over a two-sample t test?

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). The mean of the resamples is $7393,and the standard deviation of the resamples is $10,807.The observed difference in sample mean incomes was $6987.What is the bootstrap estimate of the bias?

Which of the following statements is TRUE regarding inference based on a small sample?

How do we calculate the P-value for a permutation test?

Suppose you are performing bootstrapping using computer software.The software output gives the mean of the original data set to be 15.The software output gives the bias to be 2.What is the mean of the resample means?

Which of the following statements about permutation resamples and tests is/are FALSE?

The general procedure for bootstrapping calls for resamples from the data ______.

A real estate agency with property all throughout the Midwest is interested in home prices within the state of Michigan.The average price of a simple random sample of residential properties in the Upper Peninsula is compared to the average price of a simple random sample of residential properties in the Lower Peninsula.From the collected data,2440 resamples without replacement are taken.The distribution of the difference in means based on the resamples is shown below (in thousands of dollars). The observed difference in sample mean prices is $300,000.What is the estimate of the P-value?

Suppose we use a permutation test to test a one-sided alternative hypothesis and estimate the P-value to be 0.02.If we used 1600 resamples,what is the approximate standard deviation of the estimated P-value?

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.Which of the following statements about this situation is/are TRUE?

Is the bootstrap distribution from a very small sample reliable?

Bootstrapping can be performed on the ______.

A real estate agency with property all throughout the Midwest is interested in home prices within the state of Michigan.The average price of a simple random sample of residential properties in the Upper Peninsula is compared to the average price of a simple random sample of residential properties in the Lower Peninsula.From the collected data,2440 resamples without replacement are taken.The distribution of the difference in means based on the resamples is shown below (in thousands of dollars). What type of resampling method was used in this scenario?

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.Which of the following could not be the means of the first three resamples?

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). What type of resampling method was used in this scenario?

How is the bootstrap standard error calculated?

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 15 corporate executives.Summary statistics are given below. What is the bootstrap,t,95% confidence interval for the 25% population trimmed mean?

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 95% bootstrap confidence interval for the 25% trimmed mean?

The bootstrap distribution for means calculated from a large number of resamples should be ______.