uppose a group compiled historical data about Old Faithful Geyser (Yellowstone National Park) from 1870 to 1987. Let x1 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 9,360 observations, the sample mean interval was x1 = 61.4 minutes. Let x2 be a random variable that represents the time interval in minutes between Old Faithful eruptions for the years 1983 to 1987. Based on 25,457 observations, the sample mean time interval was x2 = 69.0 minutes. Historical data suggest that 1 = 9.05 minutes and 2 = 12.90 minutes. Let 1 be the population mean of x1 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 1 − 2? Explain. Student's t should be used because 1 and 2 are unknown. Student's t should be used because 1 and 2 are known. Standard normal should be used because 1 and 2 are known. Standard normal should be used because 1 and 2 are unknown. Correct: Your answer is correct. (b) Compute a 99% confidence interval for 1 − 2 (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.) Incorrect: Your answer is incorrect. minutes
