Question

Athletes performing in bright sunlight often smear black eye grease under their eyes to reduce glare. 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-pair design. Here are the differences in sensitivity, where the difference is defined as eye grease minus without eye grease:

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

Does eye grease work? Let m be the mean sensitivity difference in the population. We want to know whether eye grease increases sensitivity, on the average (i.e., m > 0).

(A) State the null and alternative hypotheses.

(B) Assume that the “simple conditions” hold. 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 St dev = 0.22. Carry out a test of significance at the a = 0.05 level by following the State, Plan, Solve, and Conclude of the four-step process.

Vigorous exercise is associated with several years of longer life (on the average). Whether mild activities like slow walking are associated with a longer life is not clear. Suppose that the added life expectancy associated with slow walking daily for 10 minutes is just one month. A statistical test is more likely to find a significant increase in mean life for those who slow walk daily if

(A) it is based on a very large random sample.

(B) it is based on a very small random sample.

(C) the size of the sample has little effect on significance for such a small increase in life expectancy

Answer 1