In a little over a month, from June 5, 1879, to July 2, 1879, Albert Michelson measured the velocity of light in air 100 times (Stigler, Annals of Statistics, 1977). Today we know that the true value is 299,734.5 km/sec. Michelson’s data have a mean of 299,852.4 km/sec with a standard deviation of 79.01. 

(a) Find a two-sided 95% confidence interval for the true mean (the true value of the speed of light).

(b) What does the confidence interval say about the accuracy of Michelson’s measurements?