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 three hours facing into bright sun, both with and without eye grease. This is a matched pairs design. Here are the differences in sensitivity, with eye grease minus without eye grease. 0.06 0.64 −0.12 −0.06 −0.18 0.15 −0.17 0.03 0.04 0.03 0.42 0.25 −0.11 0.28 0.05 0.29 We want to know whether eye grease increases sensitivity on the average. (a) What are the null and alternative hypotheses? H0: μ = 0 Ha: μ < 0 H0: μ = 0 Ha: μ ≠ 0 H0: μ = 0.1 Ha: μ > 0.1 H0: μ = 0 Ha: μ > 0 Say in words what mean μ your hypotheses concern. μ is the mean sensitivity difference in the population. μ is the mean sensitivity difference in the sample. μ is the mean sensitivity in the population. μ is the average of mean sensitivity differences in many SRS's of size 16 from the population. (b) Suppose that the subjects are an SRS of all young people with normal vision, that contrast differences follow a Normal distribution in this population, and that the standard deviation of differences is σ = 0.22. Carry out a test of significance. STATE: True or False: We want to know whether eye grease has a significant impact on eye sensitivity. True False PLAN: We test the hypotheses stated in (a). SOLVE: What is the value of the test statistic? (Round your answer to two decimal places.) z = SOLVE (continued): What is the P-value of the test? (Use Table A and round your answer to four decimal places.) P-value = CONCLUDE: What is your conclusion? The sample gives significant evidence, at the α = 0.05 level, that eye grease does not increase sensitivity. The sample gives significant evidence, at the α = 0.05 level, that eye grease increases sensitivity. The sample gives strong evidence, at the α = 0.01 level, that eye grease increases sensitivity. The data do not provide good evidence that eye grease increases sensitivity.

Answer 1

The statistical software output for this problem is:

Hence,

a) Hypotheses:

H0: μ = 0 Ha: μ > 0

μ is the mean sensitivity difference in the population.

b) State: True

Plan: z = 1.82

P - value = 0.035

The sample gives significant evidence, at the α = 0.05 level, that eye grease increases sensitivity.