Eight observations were conducted on a scale model of a lunar vehicle with the average observed speed x = 102.2 meters per second. Assume that speed is normally distributed with known standard deviation = 4 meters per second.

a) Test the hypothesis: H0: =100 versus: H1: < 100 using = 0.05.

b) Compute the power of the test if the true mean speed is as low as 95 meters per second.