**One-sample t test of Speed of Light Data**

In this activity, you will be performing a one sample t-test analysis on the velocities of light in air collected by the physicist A. A. Michelson in 1879. These measurements were made available at the Data and Story Library at Carnegie Mellon University. These measurements were grouped into five trials of 20 measurements each. The numbers are in m/sec, and have had 299,000 subtracted from them.

Because the speed of light is a physical constant, we know (to a very close approximation) the "true" value that Michelson was trying to measure. The true value of the speed of light is 299,734.5 meters per second. It is therefore possible to test the null hypothesis that the true mean = 734.5 for each of the trials separately or for all 100 determinations taken together.

Using the data set in Excel, run a two sample t-test assuming unequal variances. In the column to the right of the data set, list the standard to which the data set will be compared. You will need to copy that value down the column until you have the same number of data points. This will provide the same p-value as a single sample t-test.

1. What was the p-value of the results using all 100 determinations as the
sample?

2.
What does the p-value
show for the t-test?

3.
Is there a statistically significant difference, indicating
a flaw in Michelson's experiment?

Copyright © 2011 Central Virginia Governor's School for Science and Technology Lynchburg, VA