Consider a population of 6 students. Suppose we know the test scores of the students to be

a Find the mean y¯U and variance S2 of the population.

b How many SRS’s of size 4 are possible?

c List the possible SRS’s. For each, find the sample mean. Using Equation (2.9), find V(y¯).

d Now let stratum 1 consist of students 1–3, and stratum 2 consist of students 4–6. How many stratified random samples of size 4 are possible in which 2 students are selected from each stratum?

e List the possible stratified random samples. Which of the samples from (c) cannot occur with the stratified design?

f Find y¯str for each possible stratified random sample. Find V(y¯str), and compare it to V(y¯).

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