18 May According to the U.S. Geological Survey (USGS), the probability of a magnitude 6.7 or greater earthquake in the Greater Bay Area is 63%, about
Scenario
According to the U.S. Geological Survey (USGS), the probability of a magnitude 6.7 or greater earthquake in the Greater Bay Area is 63%, about 2 out of 3, in the next 30 years. In April 2008, scientists and engineers released a new earthquake forecast for the State of California called the Uniform California Earthquake Rupture Forecast (UCERF).
As a junior analyst at the USGS, you are tasked to determine whether there is sufficient evidence to support the claim of a linear correlation between the magnitudes and depths from the earthquakes. Download the Excel spreadsheet provided below with the data and questions.
Instructions
The variables studied in the Excel sheet are:
- Magnitude measured on the Richter scale
- Depth in km
Analyze the data and answer the questions presented on the Excel sheet.
The Excel spreadsheet contains four tabs. The first tab, labeled “data,” contains the data you will be using in your calculations. The next three tabs contain questions for you to complete. Ensure that you are completely answering all questions with steps shown, explanations, and correct formatting.
Data
| Magnitude | Depth |
| 0.75 | 7.5 |
| 0.74 | 2.5 |
| 0.64 | 14.0 |
| 1.20 | 15.5 |
| 0.70 | 3.0 |
| 2.20 | 2.4 |
| 1.98 | 14.4 |
| 0.64 | 5.7 |
| 1.22 | 6.1 |
| 0.50 | 7.1 |
| 1.64 | 17.2 |
| 1.32 | 8.7 |
| 3.87 | 9.3 |
| 0.90 | 12.3 |
| 1.76 | 9.8 |
| 1.00 | 7.4 |
| 1.26 | 17.1 |
| 0.01 | 8.8 |
| 0.65 | 5.0 |
| 1.46 | 19.1 |
| 1.62 | 12.7 |
| 1.83 | 4.7 |
| 0.99 | 6.8 |
| 1.56 | 6.0 |
| 0.40 | 14.6 |
| 1.28 | 4.9 |
| 0.83 | 19.1 |
| 1.34 | 9.9 |
| 0.54 | 16.1 |
| 1.25 | 4.6 |
| 0.92 | 4.9 |
| 1.25 | 16.3 |
| 0.79 | 14.0 |
| 0.79 | 4.2 |
| 1.44 | 5.4 |
| 1.00 | 5.9 |
| 2.24 | 15.6 |
| 2.50 | 7.7 |
| 1.79 | 16.4 |
| 1.25 | 15.4 |
| 1.49 | 4.9 |
| 0.84 | 8.1 |
| 1.42 | 7.5 |
| 1.00 | 14.1 |
| 1.25 | 11.1 |
| 1.42 | 14.8 |
| 1.35 | 4.6 |
| 1.45 | 7.1 |
| 0.40 | 3.1 |
| 1.39 | 5.3 |
| 2.40 | 6.9 |
| 0.98 | 10.1 |
| 0.34 | 2.9 |
Question 1
1a. Using the data on the 'data' tab, construct a scatterplot of the two variables in the space below. In the scatterplot, include at least the axes names and a title of the graph.
1b. Describe the scatterplot above. Identify the two variables and any correlation that you observe in the scatterplot above. Explain your answer.
Question 2
| r | ||
| CV of r |
2a. Calculate the value of the linear correlation coefficient r and the critical value of r using α = 0.05. Show your calculations for r below. Include an explanation on how you found the critical value.
2b. Determine whether there is sufficient evidence to support the claim of a linear correlation between the magnitudes and the depths from the earthquakes. Explain your answer.
Question 3
| slope | ||
| y-intercept |
3a. Find the regression equation. Let the predictor (x) variable be the magnitude. Identify the slope and the y-intercept within your regression equation. Show your calculations below. Describe how you constructed the regression equation.
3b. Is the equation a good model? Explain your answer. 3c. What would be the best predicted depth of an earthquake with a magnitude of 2.6? Include the correct units. Show your calculations below. Explain how you determined your answer.
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