Question

A standard gold bar weighs exactly 12.4 kg. We have two scales of unknown accuracy and precision. In particular, unknown to us, using Scale #1, measurements of the bar’s weight act like random draws from a ??(12.2, 0.05) distribution while, using Scale #2, measurements of the bar’s weight act like random draws from a ??(12.4, 0.2) distribution. Using each scale, we take 10 measurements and compute a 95% confidence interval for the true weight of the bar. Neither includes 12.4 kg.

a. What is the best explanation for why the confidence interval based on the Scale #1 measurements does not contain 12.4 kg?

b. What is the best explanation for why the confidence interval based on the Scale #2 measurements does not contain 12.4 kg?

Answer 1