Question

10.62 Case Study Is Old Faithful becoming less faithfuli One of the most popular natural attractions in the United States is the Old faithful geyser in Yellowstone his geyser was named for its predictable time intervals between eruptions, but is Old Faithful changing? The table lists time intervals in minutes) The four National Park. T tween eruptions for four different years. samples have means of 63.3 min, 74.3 min, 81.7 min, and 83.8 min, respectively, so i appears that the mean time interval between eruotions is not the same for the four years. Time Intervals (in min) Between Eruptions of the Old Faithful Geyser 1951 198519951996 60 90 60 86 104 95 85 52 85 91 62 58 91 62 ,-9.4 14.2 s,-13.7 s,-10.9 Based on data from geologist Rick Hutchinson and the National Park service Analvze the results Are the time intervals for the different years really different? Analyze the data at a -0.05

Answer 1

The Null and Altermative hypothesis are as follows Null hypothesis, Ho:there is no significant mean intervals for the difference years are Altemative hypothesis, Hq: there is significant mean intervals for the difference years The level of significance is, a 0.05 same are same Use Excel to perform the ANOVA one-way Anova: Single Factor SUMMARY Groups Count 1951 1985 1995 1996 SumAverage Variance 699 63.54545 97.07273 73 200.2 895 81.36364 205.8545 911 82.81818 119.5636 803 ANOVA e of Varic SS Between 2603.636 Within Gri 6226.909 MS P-value F crit 3 867.8788 5.575021 0.002719 2.838745 40 155.6727 otal 8830.545 43

From the output, observe that the F calculated value is 5.5750 The p-value is 0.0027 Compare the p-value with the level of significance. Here, the p-value is less than the level of significance so rejects the Null hypothesis. Hence, conclude that there are significant mean intervals for the difference years are same