The U.S. Geological Survey compiled historical data about OldFaithful Geyser (Yellowstone National Park) from 1870 to 1987. Letx1 be a random variable that represents thetime interval (in minutes) between Old Faithful eruptions for theyears 1948 to 1952. Based on 9580 observations, the sample meaninterval was x1 = 61.8 minutes. Letx2 be a random variable that represents thetime interval in minutes between Old Faithful eruptions for theyears 1983 to 1987. Based on 23,000 observations, the sample meantime interval was x2 = 69.2 minutes. Historicaldata suggest that σ1 = 8.49 minutes andσ2 = 11.78 minutes. Let μ1be the population mean of x1 and letμ2 be the population mean ofx2.(a) Compute a 99% confidence interval forμ1 – μ2. (Use 2 decimalplaces.)
| lower limit    | |
| upper limit    | |
(b) Comment on the meaning of the confidence interval in thecontext of this problem. Does the interval consist of positivenumbers only? negative numbers only? a mix of positive and negativenumbers? Does it appear (at the 99% confidence level) that a changein the interval length between eruptions has occurred? Manygeologic experts believe that the distribution of eruption times ofOld Faithful changed after the major earthquake that occurred in1959.
Because the interval contains only positive numbers, we can saythat the interval length between eruptions has gottenshorter.Because the interval contains both positive and negativenumbers, we can not say that the interval length between eruptionshas gotten longer.     We can not make anyconclusions using this confidence interval.Because the intervalcontains only negative numbers, we can say that the interval lengthbetween eruptions has gotten longer.
