 # Statistics Questions: Coastal and Inland Regions

Subject Mathematics General Statistics

## Question

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.

## Solution Preview

This material may consist of step-by-step explanations on how to solve a problem or examples of proper writing, including the use of citations, references, bibliographies, and formatting. This material is made available for the sole purpose of studying and learning - misuse is strictly forbidden.

The following image represents the solution for Part 1... This is only a preview of the solution. Please use the purchase button to see the entire solution

## Related Homework Solutions

General Statistics Problems \$28.00
Statistics
Mathematics
P-Value Tests
Confidence Level
Variables
Correlation
Regression Analysis
Robbery Rate
Multicolinear Pairs
Equations
Mean
Median
Standard Deviation
Statistics Questions \$35.00
Statistics
Mathematics
Evaluation
Obesity
Variables
Population
Samples
Experiment
External Validity
Study
Internal Validity
Pupils
Regular-Size Class
Math Scores
Significance Levels
General Statistics Problem \$10.00
Passenger
Airline
Binomial Distribution
Probability
Flight
Counter
Poisson
Approximation
General Statistics Questions \$23.00
Statistics
Mathematics
Class Limits
Observations
Bar Chart
Class Midpoint
Relative Frequency
Cumulative Frequency
Investments
Line Graph
Pie Chart
Least Squares in Multiple Regressions \$100.00
Mathematics
Statistics
Least Squares
Multiple Regressions
Hypothesis Testing
Predictor Variables
Sum of Squares
Residual Plots
Minitab
Partial F Test
Statistics Questions \$20.00
Statistics
Mathematics
Experiment
Students
Data Sample
Nominal Variables
Randomized Experiment
Explanatory Variables
Response Variables
Observational Study
Regression Line
Correlation Coefficient
Negative Relationship
Live Chats