We saw in Part II Review that Old Faithful eruptions do not occur at constant intervals and the intervals may vary greatly depending on the duration of the previous eruption. In that exercise, we fit a regression model, which we can now improve with t- statistics and P-values.

a)       State and test the natural null hypothesis for the slope

Here are summary statistics for the variables:

b) Create a 95% confidence interval for the mean length of time that will elapse following a 2-minute eruption. c) You arrive at Old Faithful just as an eruption ends. Witnesses say it lasted 4 minutes. Create a 95% prediction interval for the length of time you should expect to wait to see the next eruption