Suppose a group compiled historical data about Old Faithful Geyser (Yellowstone National Park) from 1870 to 1987. Let x, be a random variable that represents the time interval (in minutes) between Old Faithful eruptions for the years 1948 to 1952. Suppose that based on 9,300 observations, the sample mean interval was x, = 61.8 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 25,106 observations, the sample mean time interval was X, = 71.8 minutes. Historical data suggest that of = 8.35 minutes and o, = 12.41 minutes. Let u, be the population mean of x, and. let #2 be the population mean of x2. (a) What distribution (standard normal or Student's t) should be used to construct a confidence interval for , - H2? Explain. O Student's t should be used because of and o2 are unknown. O Student's t should be used because of and o, are known. Standard normal should be used because of and o? are known. O Standard normal should be used because of and o, are unknown. (b) Compute a 99% confidence interval for #1 - U2 (in minutes). (Enter your answer in the form: lower limit to upper limit. Include the word "to." Round your numerical values to two decimal places.) minutes (c) Comment on the meaning of the confidence interval in the context of this problem. There is a 0.99 probability that the previously found interval contains the difference between the population mean time between eruptions for the years 1948 to 1952 and the population mean time between eruptions for the years 1983 to 1987. With 99% confidence we can say that the previously found interval contains the difference between the population mean time between eruptions for the years 1948 to 1952 and the population mean time between eruptions for the years 1983 to 1987. There is a 0.99 probability that the previously found interval contains the difference between the mean time between eruptions that were in the sample for the years 1948 to 1952 and the mean time between eruptions that were in the sample for the years 1983 to 1987. Ov With 99% confidence we can say that the previously found interval contains the difference between the mean time between eruptions that were in the sample for the years 1948 to 1952 and the mean time between eruptions that were in the sample for the years 1983 to 1987