13. [-/2.28 Points] DETAILS BBUNDERSTAT13 7.4.022. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER 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 9,700 observations, the sample mean interval was x = 62.8 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 = 8.98 minutes and 2 = 11.99 minutes. Let be the population mean of x and let be the population mean of X2. (a) What distribution (standard normal or Student's t) should be used to construct a confidence interval for - ? Explain. Standard normal should be used because and 2 are known. Student's t should be used because and are unknown. Student's t should be used because and 2 are known. Standard normal should be used because and 2 are unknown. (b) Compute a 99% confidence interval for - (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. 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. 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. 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. 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. Does the interval consist of positive numbers only? Negative numbers only? A mix of positive and negative numbers? The interval contains only positive numbers. The interval contains only negative numbers. The interval contains both 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 maior carthausko that occurred in 1050 (c) Comment on the meaning of the confidence interval in the context of this problem. 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. 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. 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. 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. Does the interval consist of positive numbers only? Negative numbers only? A mix of positive and negative numbers? The interval contains only positive numbers. The interval contains only negative numbers. The interval contains both 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. At the 99% level of confidence, it appears that the population mean time between eruptions for the years 1948 to 1952 is greater than the population mean time between eruptions for the years 1983 to 1987. At the 99% level of confidence, it appears that the population mean time between eruptions for the years 1948 to 1952 is less than the population mean time between eruptions for the years 1983 to 1987. At the 99% level of confidence, we cannot conclude that there is a difference in 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. Need Help? Read It Watch It