A scale is calibrated using a weight that is known to be exactly 1 kg. Each data set below represents repeated measurements of the weight. Assume the Gauss model (measurement = true weight of 1 kg + measurement error + bias), with measurement errors following the normal curve. Since the weight actually weighs 1 kg, the null hypothesis says that the expected value should be 1 kg (no bias). For each dataset below, make a t-test to see whether the scale is properly calibrated or not. In one case, this is impossible. Which one, and why? The data is listed as the amount above or below 1kg, and the units are micrograms. a) 1, -2, 9
b) 1, -2, 9, 14, 8, 15, -1
c) 1
d) 1, 14