Question

Amblyopia (childhood cataracts) are an eye problem, present from a young age, which can be corrected using surgery and special contact lenses. However, their eyesight continues to function below average. The contrast sensitivity for each participant was measured before beginning the videogame training; they spent 40 hours playing ‘Medal of Honor’ over a one-month period; and their contrast sensitivity was measured again. A higher value for contrast sensitivity represents better eyesight.
(a) Explain why these data are paired.
(b) Conduct a hypothesis test to determine whether there was an improvement in the participants’ eyesight. You should use a significance level of α = 0.01 for this test. You must show all calculations (do not include Minitab output, but you may use Minitab to obtain summary statistics)

Answer 1

1. the data is paired beacuse the contrast sensitivity was measured before and after the experiment for the same participants.This leads to the pair (Xi,Yi) are correlated..
2. Let (Xi,Yi) pair denotes the contrast sensitivity of ith participant before and after the experiment.

here we want to test H0:Mu_d=0 vs H1:Mu_d<0

as Mu_d <0 indicates Mu_y>Mu_x which means an improvement..

we reject the null hypothesis at alpha=0.01 level if

The statistic T<t,0.99;n-1

note:Zi_0= 0 in this case