QUESTION 3 [30] 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 fren 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 Variance Number viewing show w 40 35 Region Town Industrial Zone Rural area 34 25 32 4. 16 233 24 19 88 12 Re-allocate the current sample size per stratum using 1 Nyman allocation (4) 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. 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. Estimate the proportion of households viewing show W in each of the three divisions and give the standard error of the estimates. d. Estimate the population proportion of households viewing show W and give a 95% confidence interval for the population proportion. (10) (3) (6) QUESTION 3 [30] 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 fren 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 Variance Number viewing show w 40 35 Region Town Industrial Zone Rural area 34 25 32 4. 16 233 24 19 88 12 Re-allocate the current sample size per stratum using 1 Nyman allocation (4) 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. 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. Estimate the proportion of households viewing show W in each of the three divisions and give the standard error of the estimates. d. Estimate the population proportion of households viewing show W and give a 95% confidence interval for the population proportion. (10) (3) (6)