The U.S. Geological Survey compiled historical data about Old Faithful Geyser (Yellowstone National Park) from 1870 to 1987. Let x 1 be a random variable that represents the time interval (in minutes)...

The U.S. Geological Survey compiled historical data about Old Faithful Geyser (Yellowstone National Park) from 1870 to 1987. Let
x
₁
be a random variable that represents the time interval (in minutes) between Old Faithful eruptions for the years 1948 to 1952. Based on 9320 observations, the sample mean interval was x₁
= 63.6 minutes. Let
x
₂
be a random variable that represents the time interval in minutes between Old Faithful eruptions for the years 1983 to 1987. Based on 25,691 observations, the sample mean time interval was x₂
= 73.0 minutes. Historical data suggest that σ₁
= 8.70 minutes and σ₂
= 11.64 minutes. Let μ₁
be the population mean of
x
₁
and let μ₂
be the population mean of
x
₂.