A corporation wishes to obtain information on the effectiveness of a business machine. Several division heads will be interviewed by telephone and asked to rate the equipment on a numerical scale. The divisions are in North America, Europe, and Asia. Hence, stratified sampling is used. The costs are larger for interviewing division heads located outside North America. Table Q5(c) gives the costs per interview, approximate variances of the ratings, and N that have been established. Suppose the corporation wish to take a stratified random sample of 50 division heads among the populations established. Table Q5(c) Population, N Stratum Location Costs Variance, o² 1 North America 112 9 Europe Asia 68 39 25 36 2.25 3.24 3.24 3 (i) Calculate the random sample by using the proportional allocation to choose 50 division heads among the populations established. Calculate the random sample by using the optimal allocation to choose 50 division heads among the populations established. (ii)

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A corporation wishes to obtain information on the effectiveness of a business
machine. Several division heads will be interviewed by telephone and asked to
rate the equipment on a numerical scale. The divisions are in North America,
Europe, and Asia. Hence, stratified sampling is used. The costs are larger for
interviewing division heads located outside North America. Table Q5(c) gives
the costs per interview, approximate variances of the ratings, and N that have
been established. Suppose the corporation wish to take a stratified random
sample of 50 division heads among the populations established.
Table Q5(c)
Population, N
Stratum
Location
Costs
Variance, o?
1
North America
112
9.
2.25
Europe
Asia
68
25
3.24
3
39
36
3.24
(i)
Calculate the random sample by using the proportional allocation to
choose 50 division heads among the populations established.
(ii)
Calculate the random sample by using the optimal allocation to choose
50 division heads among the populations established.
Transcribed Image Text:A corporation wishes to obtain information on the effectiveness of a business machine. Several division heads will be interviewed by telephone and asked to rate the equipment on a numerical scale. The divisions are in North America, Europe, and Asia. Hence, stratified sampling is used. The costs are larger for interviewing division heads located outside North America. Table Q5(c) gives the costs per interview, approximate variances of the ratings, and N that have been established. Suppose the corporation wish to take a stratified random sample of 50 division heads among the populations established. Table Q5(c) Population, N Stratum Location Costs Variance, o? 1 North America 112 9. 2.25 Europe Asia 68 25 3.24 3 39 36 3.24 (i) Calculate the random sample by using the proportional allocation to choose 50 division heads among the populations established. (ii) Calculate the random sample by using the optimal allocation to choose 50 division heads among the populations established.
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