ERRUPTIONS OF THE OLD FAITHFUL GEYSER
1.0 Literature Review
A geyser refers to a hot spring that occasionally due geographical processes and difference in pressure erupts hot water and steam in the air. The Old Faithful Geyser at Yellowstone National Park , Wyoming is one of the most famous geyser in the world. Given the fame of this geyser, it receives visitors from various parts of the world. For convenience of time, the national park service have erected some sign at the site to try help visitors predict the time for the occurrence of the next eruption.
The Old Faithful Geyser is not the biggest or most regular geyser in Yellowstone but it is the biggest regular geyser. It has ...view middle of the document...
The maximum height is maintained for a short time and the geyser starts waning. It is at this point that one ought to pay closer attention for them to predict the next eruption. The interval for the next eruption is based on the total duration of the current eruption.
1.2 Research Question
From previous studies there are misguided interpretations on the eruption duration and how it affects the waiting time. From mere observations we can conclude that Old Faithful has a pattern which follows a fixed set of time. The research questions that arises is;
Does the eruption and waiting time of the Old Faithful geyser follow a fixed set of time or is there a variation in the waiting time with respect to the eruption time?
1.3 Research Methodology
Data collection and sources; the data used in this study comes from Azzalin and Bowman(1990). It includes a data frame with 272 observations on 2 variables that is eruption time and waiting time. The data is heavily rounded times originally in seconds.
Of the variables the waiting time has been used as the response variable while eruption time appears as the predictor variable. These means that waiting time is seen to be determined by the time an eruption takes. So we expect that the longer the eruption period, the longer the waiting period.
This paper wishes to study the test that, under the null hypothesis, there is no variation in the waiting time. theassumptions under this hypothesis is that the interval time between one eruption to the next is fixed and do not occur by chance.
This paper shall use the one sample t-test for comparison of means and regression in testing the above hypothesis. Under the null hypothesis, the should be significant difference in the mean for the eruption time and that of waiting time. Under regression, we shall use the p-value to show if eruption time is a significant predictor of the waiting time.
1.4 Descriptive Statistics
Table 1: a summary of descriptive statistics
eruptions | | | waiting | | |
| | | | | |
Mean | | 3.487783088 | Mean | | 70.89706 |
Standard Error | | 0.069205797 | Standard Error | | 0.824316 |
Median | | 4 | Median | | 76 |
Mode | | 1.867 | Mode | | 78 |
Standard Deviation | | 1.141371251 | Standard Deviation | | 13.59497 |
Sample Variance | | 1.302728333 | Sample Variance | | 184.8233 |
Kurtosis | | -1.506167098 | Kurtosis | | -1.14153 |
Skewness | | -0.418150471 | Skewness | | -0.41863 |
Range | | 3.5 | Range | | 53 |
Minimum | | 1.6 | Minimum | | 43 |
Maximum | | 5.1 | Maximum | | 96 |
Sum | | 948.677 | Sum | | 19284 |
Count | | 272 | Count | | 272 |
From the table comparing the standard deviation, the eruption time has a smaller standard deviation than that of waiting time. the eruption time is positively skewed while the waiting time is negatively skewed. This shows that for the eruption time most of the values are to the left of the mean with extreme values...