2. (30 points) J. J. Thomson (1356-1940) discovered the electron by isolating negatively charged particles for which he could measure the mass/'charge ratio. This ratio appeared to be constant over a wide range of experimental conditions and. consequently. could be a characteristic of a new particle. His observations. from two different cathode-ray tubes that used air as the gasJ are Tube 1 (X) 0.57 0.34 0.43 0.32 0.48 0.40 0.40 Tube 2 (Y) 0.53 0.47 0.47 0.51 0.53 0.61 0.48 Assume that the populations are normal with the same variance. (a) (10 points) Find the sample means and sample variances of the two populations. (b) (10 points) Find a 90% condence interval for the difference. #1 p2. of the two means. (c) {10 points) Test that the mean charge of the electron is the same for both tubes with or = 0.05