4.19 Coding Questions

1. For this question, we’ll use the data Airq. The variable rain contains the amount of rainfall in the county in a year (in inches). For this question, we’ll be interested in testing whether or not the mean rainfall across counties in California is 25 inches.

   1. Estimate the mean rainfall across counties.

   2. Calculate the standard error of your estimate of rainfall.

   3. Calculate a t-statistic for \(H_0 : \mathbb{E}[Y] = 25\) where \(Y\) denotes rainfall. Do you reject \(H_0\) at a 5% significance level? Explain.

   4. Calculate a p-value for \(H_0: \mathbb{E}[Y] = 25\). How should you interpret this?

   5. Calculate a 95% confidence interval for average rainfall.

   6. Use the datasummary_balance function from the modelsummary package to report average air quality, value added, rain, population density, and average income, separately by whether or not the county is located in a coastal area.