Numerical Methods in Geography HW

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Two Rivers Lab GEO 370 Numerical Methods in Geography

Two prominent, free-flowing rivers of the central Sierra Nevada Mountains are the Merced and Tuolumne Rivers. They are both tributaries of the San Joaquin River. For this exercise, you will need to analyze the annual runoff data for the two rivers to determine whether they have annual runoff characteristics that are different. In other words, do the two rivers have the same, or different, hydroclimatologies? The two rivers.xls dataset contains the annual average runoff data for the rivers, and is in the Assignments folder on Blackboard. 1. You will need to determine what approach you will be using to compare the rivers’ flow. To help judge whether you should use parametric or nonparametric methods, construct a histogram for each river’s flows. Provide titles, label the axes and attach (4 pts.) HINT: You will want to classify the data using the Histogram tool of the Data Analysis Toolpak. To activate this toolpack, go to File, Options, Add-Ins, Manage (Excel Add-Ins), and check the Analysis ToolPak box. You will then have access to the Data Analysis icon in the Data tab. 2. Based on the histograms, will you use a parametric or nonparametric approach? Explain your reasoning. (3 pts.) 3. You will need to judge whether a parametric or nonparametric approach is most appropriate. Do this by constructing a time series plot containing both rivers’ discharge data (this is called a hydrograph). The hydrograph should be a line, not bar, graph. Attach the titled, labeled hydrograph. (3 pts.) 4. Based on the hydrograph, explain your decision to use a parametric or nonparametric approach (2 pts.) 5. So which inferential test will you use? Write the full, proper name of your adopted test. (1 pt.)

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6. Clearly write out the null and alternate hypotheses for this problem, using the mathematical notation. Write these hypotheses for both the one-tailed and two-tailed scenarios. (2 pts.) One-tailed: Two-tailed: 7. What sort of statistical testing seems most appropriate: one-tailed or two tailed? Clearly explain your reasoning of why a one-directional or two-directional inferential test makes the most sense. (2 pts.) 8. Now it is time to perform the statistical testing, at the 95% confidence level. Please show your work below, using a critical Z value approach (i.e., traditional hypothesis testing). You may also attach a printout of a spreadsheet in which you perform the work. But the printout is not a substitute for thoroughly showing your work below. (10 pts.)

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9. Extra credit. What is the p-value? Clearly state the likelihood of error in performing a null hypothesis rejection. (+2 pts.) 10. Based on your findings, clearly explain whether you think there is a significant difference between the two rivers’ annual flow characteristics. (2 pts.)