Reaction to a visual stimulus. How do eye and head movements relate to body movements when reacting to a visual stimulus? Scientists at the California Institute of Technology designed an experiment to answer this question and reported their results in Nature (August 1998). Adult male rhesus monkeys were exposed to a visual stimulus (i.e., a panel of light-emitting diodes) and their eye, head, and body movements were electronically recorded. In one variation of the experiment, two variables were measured: active head movement (x, percent per degree) and body plus head rotation (y, percent per degree). The data for n = 39 trials were subjected to a simple linear regression analysis, with the following results: β1 = .88, sβ1 = .14
(a) Conduct a test to determine whether the two variables, active head movement x and body plus head rotation y, are positively linearly related. Use α = .05.
(b) Construct and interpret a 90% confidence interval for β1.
(c) The scientists want to know if the true slope of the line differs significantly from 1. Based on your answer to part b, make the appropriate inference.