Plate tectonics and the spread of the ocean floor are very important in modern studies of earthquakes and earth science in general. A random sample of islands in the Indian Ocean gave the following information, where x = age of a volcanic island in the Indian Ocean (units in 106 years) and y = distance of the island from the center of the midoceanic ridge (units in 100 km).

ˆ‘x = 415; ˆ‘y = 128; ˆ‘x2 = 30,203; ˆ‘y2 = 2558.5; ˆ‘xy = 8133
(a) Verify that the standard error of estimate Se ‰ˆ 6.50.
(b) Verify that the sample correlation coefficient r ‰ˆ 0.709. Use a 5% level of significance to test that p is positive.
(c) Verify that the equation of the least-squares line is Å· ‰ˆ 7.07 + 0.172x. Use a 5% level of significance to test that β is positive.
(d) Given that the age of a volcanic island is 55 (units in 106 years), predict how far the island is from the center of the midoceanic ridge (units in 100 km). Find an 85% confidence interval for the prediction.

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