Question

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?

Answer 1

(a) According to the Albert Michelson's measurements, two-sided 95% confidence interval for velocity of light in the air would be 299,852.4±15.5

(b) Since true velocity of light in the air is not included in the 95% confidence interval, we can say that Michelson’s measurements were not accurate.

Explanation:

Confidence Interval can be calculated using M±ME where

• M is the sample mean velocity of light in air (299,852.4)

• ME is the margin of error from the mean

And margin of error (ME) from the mean can be calculated using the formula

ME=
`(z*s)/(√(N) )` where

• z is the corresponding statistic in 95% confidence level (1.96)

• s is the sample standard deviation (79.01)
• N is the sample size (100)

Then ME=
`(1.96*79.01)/(√(100) )` ≈ 15.5

According to the Albert Michelson's measurements, 95% confidence interval for velocity of light in the air would be 299,852.4±15.5