1. An inventor claims that a device increases gas mileage by 4%. A test of the device was done by randomly selecting 10 cars (of the same make and model) that were fitted with the device and 10 cars that served as a control. These 20 cars were randomized to drivers and the mileage (mpg) was recorded for each car. A bootstrap method was used to estimate the distribution of the ratio of the mean mpg with the device to the mean mpg without the device.
Here is a summary of the bootstrap distribution for the ratio of the mean mpg (test/control):
What can we conclude from this summary?
A. Because the 95% confidence interval includes the value of 1.04, there is evidence that the device works.
B. Because the 95% confidence interval includes the value of 1.00, there is no evidence that the device works.
C. Because the mean of the bootstrap distribution is < 1.04, there is no evidence that the device works.
D. Because the mean of the bootstrap distribution is > 1, there is strong evidence that the device works.
2. Which of the following statements is correct?
A. Bootstrap methods work well with small samples if the data come from a Normal distribution.
B. Bootstrap distributions based on 2000 bootstrap samples are substantially more accurate than bootstrap distributions based on 1000 bootstrap samples.
C. Most of the variation in the bootstrap distribution comes from the random resampling done as part of the bootstrapping process.
D. Bootstrap samples will not perform well if the statistic of interest is based on only a few of the data points.
3. In which of the following situations would permutation tests be suitable?
A. For testing the equality of two population means when the standard deviations of the two populations are different.
B. For testing if the population correlation coefficient is zero between the sex of an individual and the starting salary in a job.
C. For testing the equality of two sample standard deviations when the data are not normally distributed.
D. For testing the efficacy of a drug to reduce blood pressure when each subject is measured before and after taking the drug (a matched pairs design).