Eye black Athletes performing in bright sunlight often smear black grease under their eyes to reduce glare. Does cye black work? In one experiment, 16 randomly selected student subjects took a test of sensitivity to contrast after 3 hours facing into bright sun, both with and without eye black. Here are the differences in sensitivity, with eye black mines without eye black:
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
We want to know whether cye black increases sensitivity an the average.
(a) State hypotheses, Be sure to define the parameter.
(b) Check conditions for carrying out a significance test.
(c) The $P v a l u e$ of the test is $0.047$ . Interpet this value in context.
- Interpret a Type l error and a Type ll error in context, and give the consequences of each.
- Understand the relationsonship between the significance level at a test P(Type li error), and power.

Question

Accepted Answer

(a) $H_{0} : μ d = 0$

$H_{α} : μ d > 0$

(b)Conditions for carrying out a significance test is satisfied

(c) It means that at an average $4.7 %$ of athletes differ from the athletes whose eye black does not increase the sensitivity.

Short Answer

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