Consider a population of 6 students given in the table below. We want to select a stratified sampling of size 4

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Question 1. (15 marks)

Consider a population of 6 students given in the table below. We want to select a stratified sampling of size 4 with an SRS of size 2 taken from each of the two strata.

  stratum 1

Student 1 2 3

Score 66 59 70 

  stratum 2

Student 4 5 6

Score 83 82 71

(a) (2 marks) Find the values of µ1 and µ2?

(b) (2 marks) Find the values of σ2 and σ2?

(c)    (2 marks) What are the values of V(τ ) and V(τ )

(d) (2 marks) What are the values of V(τstr )?

e.g. τstr means the estimate of τ from stratified RS.

(e) (3 marks) How many stratified random samples (RSs) are possible? List the possible stratified RSs.

(f) (2 marks) For each stratified sample, calculate µ and τ.

 

(g) (2 marks) Use the sampling distribution of µ and τ to verify that µ and τ are an unbiased

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