Finger dexterity, the ability to make precisely coordinated finger movements to grasp or assemble very small objects, is important in jewelry making. Thus, the manufacturing manager at Gemco, a manufacturer of high-quality watches, wants to develop a regression model to predict the productivity (in watches per shift) of new employees based on dexterity. He has subjected a sample of 20 current employees to the O'Connor dexterity test in which the time required to place 3 pins in each of 100 small holes using tweezers is measured.
a. Estimate the regression model: Watches = β0 + β1 Time + ε.
b. At the 5% significance level, determine if a unit of Time decreases Watches by more than 0.02. Show the relevant steps of the test.