Creativity, as any numbers of studies have shown, is very much a province of the young. Whether the focus is music, literature, science, or mathematics, an individual’s best work seldom occurs late in life. Einstein, for example, made his most profound discoveries at the age of twenty-six; Newton, at the age of twenty-three. The following are twelve scientific breakthroughs dating from the middle of the sixteenth century to the early years of the twentieth century (205). All represented high-water marks in the careers of the scientists involved.

(a) What can be inferred from these data about the true average age at which scientists do their best work? Answer the question by constructing a 95% confidence interval.

(b) Before constructing a confidence interval for a set of observations extending over a long period of time, we should be convinced that the yi’s exhibit no biases or trends. If, for example, the age at which scientists made major discoveries decreased from century to century, then the parameter μ would no longer be a constant, and the confidence interval would be meaningless. Plot “date” versus “age” for these twelve discoveries. Put “date” on the abscissa. Does the variability in the yi’s appear to be random with respect to time?

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Discoverer Year Age, y Discovery Earth goes around sun Telescope, basic laws of Copernicus 1543 40 Galileo 1600 34 1665 23 Franklin 1746 40 astronomy Principles of motion Newton gravitation, calculus Nature of electricity Burning is uniting with Earth evolved by gradua Evidence for natural 1774 31 1830 33 1858 49 Lavoisier oxygen processes selection controlling Lyell Darwin evolution Field equations for light Radioactivity Quantum theory Maxwel 1864 33 1896 34 1901 43 Special theory of relavity, Einstein 905 26 Curie Planck Mathematical foundations Schrödiner 1926 39 for quantum theory