b) One of the important reasons for carrying out the census was to know the total number of
people for proper planning by the Government. Therefore, UBOS identified six
households (least three and highest three) as shown in Table 1 and used their household
sizes to calculate the overall average household size.
Household no. HH001 HH006 HH101 HH1009 HH287 HH200
Household size 3 1 2 10 9 12
Required;
i. Obtain the possible samples of size two (n=2) that can be obtained by sampling
(a) With replacement. (4 marks)
(b) Without replacement. (4 marks)
ii. Construct the Sampling distribution of sample means in both cases i (a) and i (b)
respectively. (8 marks)
iii. Calculate the average of the six households from the sample means. (4 marks)
Hint: use the expectations.
iv. Define the terms central limit theorem and finite population multiplier and explain
how they can be used by UBOS in its computations.
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