Old Faithful Geyser in Yellowstone National Park derives its names and fame from the regularity (and beauty) of its eruptions. Rangers usually post the predicted times of eruptions for visitors. R. A. Hutchinson, a park geologist, collected measurements of the eruption durations (in minutes) and the subsequent time intervals before the next eruption (in minutes) over an 8-day period. Help rangers use the data to explain the relationship between duration and subsequent time to the next eruption. Then, help them use that relationship to predict when next eruptions will occur. Provide the ranger with an estimate of the mean length of time until the next eruption after one lasting for 4 minutes. Also, provide the ranger with a prediction of how many minutes visitors will have to wait after a future eruption lasting 4 minutes. Be sure to give the rangers appropriate uncertainty intervals to go with estimates and/or predictions. Also, provide the rangers with a plot. Hints:

1. You can ignore \DATE" for the purpose of doing the analysis, but I expect you to discuss it when you are checking assumptions within the Statistical Procedures Used section. What plot could you make to help assess independence?

2. You will really have three different summary statements to make in your Summary of Statistical Findings. One describing the relationship (and evidence for there being a relationship), one describing estimation of a mean, and one describing a prediction.

3. Use the Big Bang Case Study for example R-code.