Exercise 55

Here are the data from the researcher studying the reaction times of rats. He has a requirement that the maze take about a minute to complete on average.

? ? ? ? ? Time (sec)38.4 .................... 57.646.2 .................... 55.562.5 .................... 49.538.0 .................... 40.962.8 .................... 44.333.9 .................... 93.850.4 .................... 47.935.0 .................... 69.252.8 .................... 46.260.1 .................... 56.355.1

A student resampled the Maze times from Exercise 55 1000 times. The histogram shows the distributions of the means, and a summary of the quantiles is shown below it.

a) Find a 99% bootstrap confidence interval for the true mean time it takes to complete the maze.

b) Why is the sampling distribution slightly skewed to the right?

c) How does the skewness affect the confidence interval?

d) What does the confidence interval say about the hypothesis that it takes a minute on average?

0.05% 0.1% 0.5% 1% 5% 50% 95% 99% 99.5% 99.9% 99.95% 44.657 44.985 45.271 46.119 47.642 52.021 57.220 59.363 59.939 62.088 63.132