The US Geological Survey compiled historical data about Old

The U.S. Geological Survey compiled historical data about Old Faithful Geyser (Yellowstone National Park) from 1870 to 1987. Let x₁ be a random variable that represents the time interval (in minutes) between Old Faithful eruptions for the years 1948 to 1952. Based on 9560 observations, the sample mean interval was x₁ = 63.8 minutes. Let x₂ be a random variable that represents the time interval in minutes between Old Faithful eruptions for the years 1983 to 1987. Based on 23,000 observations, the sample mean time interval was x₂ =69.0 minutes. Historical data suggest that ₁ = 8.14 minutes and ₂ = 12.34 minutes. Let ₁ be the population mean of x₁ and let ₂ be the population mean of x₂.

(a) Compute a 99% confidence interval for ₁ – ₂. (Use 2 decimal places.)

Solution