Assume that the standard deviations of the tin-coating weights determined by any one of the 4 laboratories have the common value \(\sigma=0.012\), and that it is desired to be \(95 \%\) confident of detecting a difference in means between any 2 of the laboratories in excess of 0.01 pound per base box. Show that these assumptions lead to the decision to send a sample of 12 disks to each laboratory.