Chapter 7.4, Problem 9Q

Creativity, as any number 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 $\left(217\right)$. All represented high-water marks in the careers of the scientists involved.

Discovery	Discoverer	Year	Age, $y$
Earth goes around sun	Copernicus	1543	40
Telescope, basic laws of astronomy	Galileo	1600	34
Principles of motion, gravitation, calculus	Newton	1665	23
Nature of electricity	Franklin	1746	40
Burning is uniting with oxygen	Lavoisier	1774	31
Earth evolved by gradual processes	Lyell	1830	33
Evidence for natural selection controlling evolution	Darwin	1858	49
Field equations for light	Maxwell	1864	33
Radioactivity	Curie	1896	34
Quantum theory	Planck	1901	43
Special theory of relativity, $E=m{c}^2$	Einstein	1905	26
Mathematical foundations for quantum theory	Schrodinger	1926	39

• (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 $y_i$’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 $\mu$ 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 $y_i$’s appear to be random with respect to time?