Question 8-2 atic a the met as selecting generally no very good representative s
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Question 8-2
atic a the met as selecting generally no very good representative systematie in which system- data exhibit a pattern, then of of population. However, dom population very bad, pending on the quality sample is likely to be very good or de if the nature of the pattern. Cluster sampling is generally used because of the convenience and cost-effectiveness in collecting such a data. However, contrary to the case of sampling, if data values within each cluster are and clusters are reasonably similar, a sample cluster sampling is likely to be a very good representative of the population data. EXERCISES 8-1 TO 8-2 8-1. Discuss advantages and disadvantages of different probability sampling methods. 8-2. The table below lists the top 20 companies in Canada during 2000, together with their total revenue (in thousands of dollars)Explanation / Answer
13, 08, 01, 05, 06, 17, 17, 13, 18, 11
Hence our sample using SRN is (Bombardier Inc., Imperial Oil, Royal Bank of Canada, Bank of Montreal, Canadian Pacific, Petro-Canada, Magna International, Pan Canadian Petroleum).
(b) The first 8, 2-digit numbers in the range 00-19, starting from beginning of row 7 are:
13, 08, 01, 05, 06, 17, 17, 13,
Hence our sample using SRR is (Bombardier Inc., Imperial Oil, Royal Bank of Canada, Bank of Montreal, Canadian Pacific, Petro-Canada, Petro-Canada, Bombardier Inc.).
(c) Here N = 20, n = 8.
So k = (N/n) = 20/8 = 2.5. We shall choose k = 2.
Starting number is 13.
The systematic sample will include 13th, 15th, 17th, 19th, 1st, 3rd, 5th and 7th data units.
The sample is (Toronto-Dominion Bank, Alberta Energy Co., Talisman Energy, Magna International, BCE Inc., Cdn. Imp. Bank of Commerce, Thompson Corp., Canadian Pacific).
(d) Group 1 (revenue more than $16 billion): 00, 01, 02, 03, 05, 06, 08, 12, 13.
Group 2 (revenue in the range of $8 billion to $16 billion): 07, 09, 10, 15, 17, 18, 19.
Group 3 (revenue less than $8 billion): 04, 11, 14, 16.
Group 1 contains 9 units, group 2 contains 7 units, and group 3 contains 4 units. We shall attempt to choose sample sizes proportional to sizes of the groups (strata).
Hence we shall choose samples of size
(9/20) * 9 = approx 4,
(7/20) *9 = approx 3, and
(4/20) * 9 = approx 2,
for groups 1, 2 and 3 respectively.
We start from the beginning of row 7 of Appendix B and choose random numbers along the row. We first choose a sample from group 1, then a sample from group 2 and then a sample from group 3. This gives us the following samples:
Sample from group 1: 13, 08, 01, 05.
Sample from group 2: 17, 18, 09.
Sample from group 3: 04, 11.
So, the resultant sample is (Bombardier Inc., Imperial Oil, Royal Bank of Canada, Bank of Montreal, Petro-Canada, Magna International, Quebecor Inc., Thompson Corp., Pan Canadian Petroleum).
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