For this lab you should submit, on Blackboard, your .Rmd and .docx-files at the end of the lab hour.

Test objects and confidence interval values

We will learn how to perform different tests in the next couple of weeks. All of the functions we will learn produce a test object in R. Test objects all share some features. Suppose we have assigned the name test to a particular test object, then

Attribute	Contains
test$statistic	The value of the test statistic
test$p.value	The \(p\)-value of the test
test$conf.int	The confidence interval for the test
test$alternative	The alternative hypothesis type (upper / lower / two-tailed) of the test
test$method	The test type

Many tests expect a key/value pair of columns to allow the ~ way of writing test commands.

Task Load the dataset mpg using data(mpg)

Task Create a new dataset mpg.cty.hwy using gather that contains a key column type and a value column mpg with the columns cty and hwy from the original data.

Task Construct a test object using

t.cty.hwy = t.test(mpg ~ type, data=mpg.cty.hwy)

Task Write out the test object itself (using a code block with just the test object name itself alone on a line). Describe the printout and what information you can read from it.

Task Using the $ syntax in the table above, extract the p-value and confidence interval from the test.

For some functions we have been using, we need a data.frame. The library broom contains functions for converting various objects into data.frames. Most useful is the function tidy that converts most things into a data.frame.

Task Load the library broom and use the function tidy to create a data.frame from t.cty.hwy.

Bootstrap confidence intervals

Recall that we can use bootstrap to get empirical distributions of sample statistics. This can be used to create a special kind of confidence intervals directly from the data.

For instance, one might do the following to get a 10% confidence interval for the mean city milage:

cty.mean = do(1000)*mean(~cty, data=mpg %>% sample_n(50))
cty.boot.ci = quantile(~mean, probs=c(.05, .95), data=cty.mean)

Task Change the above code to find a 5% confidence interval for the mean highway mileage.