(3b) Do these observations suggest that Old Faithful Geyser's eruption-interval is less than 100 minutes on average? Set up hypotheses. (5 points) Ho : Ha : (3c) Test your hypotheses with the significance level of a = 0.01. Justify all steps both algebraically and graphically. (10 points for the algebra and 5 points for the graph)3. The following data table shows the eruption-duration and the interval between the erup- tions of Old Faithful Geyser in minutes, measured by a visitor over a weekend. 1 2 3 4 5 6 7 | s 9 1o 11 12 Mean SD Duration 1.7 1.9 2.0 2.3 3.1 3.4 3.5 I 4.0 4.3 4.5 4.7 4.9 3.358 1.156 Interval 55 49 51 53 57 75 80 | 75 34 76 93 76 68.750 14.845 (3a) Estimate the 96% condence interval of the eruption-duration. Justify all steps both algebraically and graphically. (10 points for the algebra and 5 points for the graph)