Old Faithful, the most reliable geyser in Yellowstone National Park can shoot up to 8,400 gallons of boiling water to a height of about 150 feet. More than 1,000,000 eruptions have been recorded. There is evidence that eruptions of Old Faithful can best be predicted by knowing the duration of the previous eruption. The results from regression analysis of Waiting Time (minutes) between eruptions versus Duration (minutes) of the previous eruption for a random sample of 222 eruptions are shown below. Waiting Time 95 Statistic Duration WaitingTime Mean 3.576 71.009 75 Standard Deviation 1.084 12.799 55 Sample Size 222 35 Correlation 0.877 1.5 2.5 3.5 Duration 4.5 5.5 Slope 10.358 Intercept 33.967 Predictor Coef SE Coef T P Intercept 33.967 1.428 23.79 0.0000 Duration 10.358 0.382 27.10 0.0000 Predicted Values for New Observations Duration Fit 4 75.4 SE Fit 0.444 95% CI 95% PI (74.5, 76.3) (63.2, 87.6) 1. At the 0.05 level of significance, is there evidence of a linear relationship between Duration and Waiting Time? Ho: Ha: Test statistic = P-value = Decision: Reject Ho Do not reject Ho Why you made this decision: Conclusion: There is not enough weak moderate strong overwhelming (choose one) statistical evidence of a linear relationship between Duration and Waiting Time. 2. Calculate and interpret the coefficient of determination. Coefficient of determination = Interpretation: 3. What is the equation of the fitted line? 4. Fill in the blanks in the following interpretation of the slope of the fitted line. As the duration of the previous eruption increases by the waiting time between eruptions increases by about minute(s), minutes on average. 5. If you just witnessed an eruption that lasted 4 minutes, how long do you predict you'll have to wait to see the next eruption? Predicted waiting time = minutes 6. So, you waited, and the next eruption came in 79 minutes. Is this an unusually long waiting time? Unusually long waiting time: Yes No Explanation: