The U.S. Geological Survey compiled historical data about Old Faithful Geyser (Y

Question

The U.S. Geological Survey 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. Based on 9780 observations, the sample mean interval was x1 = 62.0 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 25,106 observations, the sample mean time interval was x2 = 70.6 minutes. Historical data suggest that 1 = 9.33 minutes and 2 = 12.83 minutes. Let 1 be the population mean of x1 and let 2 be the population mean of x2. (a) Compute a 95% confidence interval for 1 – 2. (Use 2 decimal places.) lower limit upper limit

Explanation / Answer

Given n1 =9780 X1 = 62.0    1= 9.33

            n2 =25106 X2 = 70.6    2= 12.83

S.E(X1 -   X2) = (12/n1)+ (22/n2) = ((9.33)2/9780)+ ((12.83)2/25106)

                              = 0.0155 = 0.1245

95% confidence interval is

X1 -   X2 ± 1.96 * S.E(X1 -   X2)

62.0 - 70.6 ± 1.96 * 0.1245

8.2 ± 1.96 * 0.1245

[7.9560 , 8.4440]

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