Question 8.71
georgiarain
71. A Rainy Month in Georgia? The following table represents the total rainfall (in inches) for the month of February 2011 for a random sample of 10 locations in Georgia.5 Assume .
| Location | Rainfall (inches) |
Location | Rainfall (inches) |
|---|---|---|---|
| Athens | 4.72 | Atlanta | 4.25 |
| Augusta | 4.31 | Cartersville | 3.03 |
| Dekalb | 2.96 | Fulton | 4.36 |
| Gainesville | 4.06 | Lafayette | 3.75 |
| Marietta | 3.20 | Rome | 3.26 |
- Assess the normality of the data, using a normal probability plot.
- Assuming that the rainfall amounts are normally distributed, construct and interpret a 95% confidence interval for the population mean rainfall in inches.
- Calculate and interpret the margin of error for the confidence interval in part (b).
- How large a sample size do we need to estimate to within 0.1 inch with 95% confidence?
8.1.71
(a) The normal probability plot indicates an acceptable level of normality.
(b) (3.393, 4.187). We are 95% confident that the population mean rainfall in Georgia lies between 3.393 inches and 4.187 inches. (c) inch. We can estimate the population mean rainfall in Georgia to within 0.397 inch with 95% confidence. (d) 158 locations