Problem: You are a research assistant who is investigating spatial variations in rainfall for selected highland areas of Costa Rica. As part of the research team, your task is to examine rainfall totals during the month of November in four regions: A, B, C, and D from observations obtained from n=10 randomly selected weather stations in each region. Table 1 below shows the average rainfall totals (X) in inches (rounded to the nearest .1”) for the n=10 randomly selected stations in each of four geographic regions of Costa Rica for the month of November (for randomly selected years during the period: 1982-2011):
A B C D
10.0 12.4 14.5 14.0
9.5 13.5 14.8 17.5
10.0 9.4 15.6 16.0
10.0 10.0 13.8 17.0
13.5 14.0 12.8 16.5
15.0 15.0 13.4 18.2
11.0 11.0 9.0 15.2
10.5 13.2 11.0 16.0
12.5 10.5 12.5 15.4
8.0 11.0 12.6 14.2
Note: Region D is a coastal region; Regions A, B and C are inland regions.
Part 1. ANOVA: Is there statistical evidence (at the 95% confidence level) to support the claim that no distinct differences exist in the amount of total rainfall observed in the interior regions A, B, and C? Test the null hypothesis of equality of means between the three inland regions-- Is the mean total rainfall during the month of November equal in regions A, B, and C (for the period in question)? Discuss your findings. Is there statistical evidence at the 95% confidence level to support the claim that all four regions (A, B, C, and D) have equal mean total rainfall amounts for the month of November? Discuss your findings and the implications?
Part 2. Using the sample data above, implement a statistical test (at 95% confidence) to evaluate the null hypothesis that the average total rainfall in region C during the month of November is equal (i.e., not significantly different) to the average total rainfall in region D versus the alternative hypothesis that the average total rainfall in region C is significantly less than the average total rainfall in region D– In short, carry out an equality of means t-test procedure under the assumption of unequal variance using a “one-tailed” test. Discuss the results.
Part 3. Using the sample data in Table 1, carry out an additional “one-tailed t-test” to compare the average total rainfall amounts in regions C and D (just as you did in part 2) under the assumption of equal variance. Discuss the results.
Part 4. Is there any supporting statistical evidence of “equal variance” in the total rainfall amounts for from the data obtained from the n=10 weather stations during the month of November in regions C and D for the period in question (using a one-tailed F-ratio test for equality of variance at the 95% confidence)? Discuss your findings.
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