Athletes performing in bright sunlight often smear black eyegrease under their eyes to reduce glare. In one study, 16 studentsubjects took a test of sensitivity to contrast after three hoursfacing into bright sun, both with and without eye grease. This is amatched-pair design. Here are the differences in sensitivity, wherethe difference is defined as eye grease minus without eyegrease:

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 meansensitivity difference in the population. We want to know whethereye 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 thesubjects are an SRS of all young people with normal vision, thatcontrast differences follow a Normal distribution in thispopulation, and that the standard deviation of differences isSt dev = 0.22. Carry out a test of significance atthe 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 longerlife (on the average). Whether mild activities like slow walkingare associated with a longer life is not clear. Suppose that theadded life expectancy associated with slow walking daily for 10minutes is just one month. A statistical test is more likely tofind a significant increase in mean life for those who slow walkdaily 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 forsuch a small increase in life expectancy