Question

Athletes performing in bright sunlight often smear black eye grease under their eyes to reduce glare. Does eye grease work? In one study, 1616 student subjects took a test of sensitivity to contrast after three hours facing into bright sun, both with and without eye grease. Greater sensitivity to contrast improves vision and glare reduces sensitivity to contrast. This is a matched pairs design. The differences in sensitivity, with eye grease minus without eye grease is given.

Differences in sensitivity, with eye grease minus without eye grease
0.070.07	0.640.64	−0.12−0.12	−0.05−0.05	−0.18−0.18	0.140.14	−0.16−0.16	0.030.03
0.050.05	0.020.02	0.430.43	0.240.24	−0.11−0.11	0.280.28	0.050.05	0.290.29

How much more sensitive to contrast are athletes with eye grease than without eye grease? Give a 99%99% confidence interval to answer this question. (Enter your answers rounded to four decimal places.)

Lower bound =

Upper bound =

Answer 1

Solution :

Given data d as 0.07,0.64,-0.12,-0.05,-0.18,0.14,-0.16,0.03,0.05,0.02,0.43,0.24,-0.11,0.28,0.05,0.29

=> mean d-bar = sum of terms/number of terms

= 1.62/16

= 0.1013

=> standard deviation Sd-bar = 0.2263

=> df = n - 1 = 15

=> for 99% confidence interval, t = 2.947

=> A 99% confidence interval is

=> d-bar +/- t*Sd-bar/sqrt(n)

=> 0.1013 +/- 2.947*0.2263/sqrt(16)

=> (-0.0654 , 0.2680)

==> Lower bound = -0.0654

==> Upper bound = 0.2680