An advertising firm, interested in determining how much to emphasize c Industrial zone and Rural. The firm decided to conduct a sample survey to television and proportion of households viewing show W. There are 310, stratified random sampling method is suitable to obtain the observations a below summarizes the results of the survey. Sample Size Region Town 40 Industrial Zone 16 Rural area 24 a. Re - allocate the current sample size per stratum using Nyman allocation Proportional allocation II. Optimum allocation. Assume that cost of obtaining a s b. Estimate the average and total number of hours that all households

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An advertising firm, interested in determining how much to emphasize on television advertising in a certain region of three major divisions referred to as Town A,
Industrial zone and Rural. The firm decided to conduct a sample survey to estimate the average number of hours each week that a house hold within the region watch
television and proportion of households viewing show W. There are 310, 124 and 186 households in town A, industrial zone and rural area; respectively. Assume that a
stratified random sampling method is suitable to obtain the observations and that the advertising firm has enough resource to interview 80 to 85 households. The Table
below summarizes the results of the survey.
Sample
Size
Sample
Mean
Number
Variance
viewing show W
Region
Town
40
34
35
32
Industrial Zone
16
25
233
4
Rural area
24
19
88
12
a. Re - allocate the current sample size per stratum using
Nyman allocation
Proportional allocation
Optimum allocation Assume that cost of obtaining a single observation from each of the divisions are R2.25, R 1.44 and R4, respectively
b. Estimate the average and total number of hours that all households spend viewing TV in the region and the standard error of the two estimators.
c. Estimate the proportion of households viewing show W in each of the three divisions and give the standard error of the estimates
Transcribed Image Text:An advertising firm, interested in determining how much to emphasize on television advertising in a certain region of three major divisions referred to as Town A, Industrial zone and Rural. The firm decided to conduct a sample survey to estimate the average number of hours each week that a house hold within the region watch television and proportion of households viewing show W. There are 310, 124 and 186 households in town A, industrial zone and rural area; respectively. Assume that a stratified random sampling method is suitable to obtain the observations and that the advertising firm has enough resource to interview 80 to 85 households. The Table below summarizes the results of the survey. Sample Size Sample Mean Number Variance viewing show W Region Town 40 34 35 32 Industrial Zone 16 25 233 4 Rural area 24 19 88 12 a. Re - allocate the current sample size per stratum using Nyman allocation Proportional allocation Optimum allocation Assume that cost of obtaining a single observation from each of the divisions are R2.25, R 1.44 and R4, respectively b. Estimate the average and total number of hours that all households spend viewing TV in the region and the standard error of the two estimators. c. Estimate the proportion of households viewing show W in each of the three divisions and give the standard error of the estimates
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