11.3.2 Two groups are to be selected with equal probability without replacement from the following four groups. Once a group has been selected into the sample all units within the group are included in the sample.
Groups Measurements
$G_1$: 11, 12, 15
$G_2$: 14, 18, 21
$G_3$: 23, 29, 31
$G_4$: 29, 30, 36
(a) How many different samples can arise with this sampling scheme?
(b) If $\bar{y}$ is the equally weighted mean of the 6 sample observations, write down the sampling distribution of $\bar{y}$.
(c) Show that $\bar{y}$ is unbiased for $\bar{Y}$.
(d) Calculate $Var(\bar{y})$.
