The U.S. Geological Survey compiled historical data about Old Faithful Geyser (Yellowstone National Park) from 1870 to 1987. Let be a random variable that represents the time interval (in minutes) between Old Faithful eruptions for the years 1948 to 1952. Based on 9120 observations, the sample mean interval was x, = 64.8 minutes. Let x, be a random variable that represents the time interval in minutes between Old Faithful eruptions for the years 1983 to 1987. Based on 23,234 observations, the sample mean time interval was x2 = 69.8 minutes. Historical data suggest that 0 = 8.28 minutes and o2 = 11.57 minutes. Let Hy be the population mean of X1 and let uz be the population mean of x2. (a) Compute a 95% confidence interval for - M2. (Use 2 decimal places.) lower limit upper limit (b) 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 95% 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.