One measure of the meat quality of pigs is backfat thickness. Suppose two researchers, Jones and Smith, are planning to measure backfat thickness in two groups of pigs raised on different diets. They have decided to use the same number (n) of pigs in each group and to compare the mean backfat thickness using a two-tailed t test at the 5% significance level. Preliminary data indicate that the SD of backfat thickness is about 0.3 cm.
When the researchers approach a statistician for help in choosing n, she naturally asks how much difference they want to detect. Jones replies, "If the true difference is 1/4 cm or more, I want to be reasonably sure of rejecting H0" Smith replies, "If the true difference is 1/2 cm or more, I want to be very sure of rejecting H0."
If the statistician interprets "reasonably sure" as 80% power, and "very sure" as 95% power, what value of n will she recommend
(a) To satisfy Jones's requirement?
(b) To satisfy Smith's requirement?