Yellowstone National Park: Old Faithful Geyser The U.S. Geological Survey compiled historical data about Old Faithful Geyser (Yellowstone National Park) from 1870 to 1987. Some of these data are published in the book The Story of Old Faithful, by G. D. Marler (Yellowstone Association Press). Let x1 be a random variable that represents the time interval

(in minutes) between Old Faithful’s eruptions for the years 1948 to 1952. Based on 9340 observations, the sample mean interval was x1 5 63.3 minutes. Let x2 be a random variable that represents the time interval in minutes between Old Faithful’s eruptions for the years 1983 to 1987. Based on 25,111 observations, the sample mean time interval was x2 5 72.1 minutes.

Historical data suggest that s1 5 9.17 minutes and s2 512.67 minutes. Let m1 be the population mean of x1 and let m2 be the population mean of x2.

(a) Check Requirements Which distribution, normal or Student’s t, do we use to approximate the x1 2x2 distribution? Explain.

(b) Compute a 99% confidence interval for m1 2m2.

(c) Interpretation Comment on the meaning of the confidence interval in the context of this problem.
Does the interval consist of positive numbers only? negative numbers only? a mix of positive and negative numbers? Does it appear (at the 99%
confidence level) that a change in the interval length between eruptions has occurred? Many geologic experts believe that the distribution of eruption times of Old Faithful changed after the major earthquake that occurred in 1959.AppendixLO1