Athletes performing in bright sunlight often smear black eye grease under their

Question

Athletes performing in bright sunlight often smear black eye grease under their eyes to reduce glare. Does eye grease work? In one study, 16 student subjects took, a test of sensitivity to contrast after 3 hours facing into bright sun, both with and without eye grease. This is a repeated measure design where each subject was measured under each condition. The differences in sensitivity (i.e. with eye grease minus without eye grease) are: 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 Suppose that the subjects are a simple random sample of all young people with normal vision. Furthermore, contrast differences follow a normal distribution with a population standard deviation of differences being 0.22. Does eye grease cause increase sensitivity on average? Give a justification as to why or why not.

Explanation / Answer

std error =std deviation/(n)1/2 =0.055

hence test stat z=(X-mean)/std error = (0.10125-0)/0.055 =1.8409

critical value at 0.05 level =1.645

as test stat is higher then critical value we reject null hypothesis and conclude that eyw grease causes increase sensitivity

d 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 0.10125

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