Refer to data on ages and depths of fish fossils for the first site presented in the preceding exercise.
a. The t statistic for regressing age on depth is 42.80. Can we conclude that the P-value is small, not small, or borderline?
b. Which interval should contain the mean age of all fossils whose depth is 200 mbsf: a confidence interval or a prediction interval?
c. When depth equals 200 mbsf, predicted age is 55.3 million years old. Use the fact that spread s about the regression line is 1.2 to construct an approximate 95% prediction interval for age of an individual fossil whose depth is 200 mbsf.
d. The actual prediction interval is (52.8, 57.9). Comment on whether your approximate interval from part (c) came fairly close to this.
e. When depth equals 200 mbsf, predicted age is 55.3 million years old. Use the fact that spread s about the regression line is 1.2 and sample size is 25 to construct an approximate 95% confidence interval for mean age of all fossils whose depth is 200 mbsf.
f. The actual confidence interval is (54.9, 55.8). Comment on whether your approximate interval from part (e) came fairly close to this.
g. Would a confidence interval for mean age of all fossils whose depth is 100 mbsf be narrower, wider, or about the same width as the confidence interval for mean age of all fossils whose depth is 200 mbsf?
h. If we have no information about a fossil's depth, we would have to guess its age to be somewhere in the interval mean plus or minus 2 standard deviations in age: 55.5 + 2(10.5) = (34.5, 76.5). Explain why this interval is so much wider than the prediction interval you constructed in part (c).