Exercise Chapter 5 Buku Elementary Survey Sampling

5.5 A corporation wishes to obtain information on the effectiveness of a business machine. A number of division heads will be interviewed by telephone and asked to rate the equipment on a numerical scale. The divisions are located in North America, Europe, and Asia. Hence, stratified sampling is used. The costs are larger for interviewing division heads located outside North America. The accompanying table gives the costs per interview, approximate variances of the ratings, and N that have been established. The corporation wants to estimate the average rating with . Choose the sample size n that achieves this bound, and find the appropriate allocation

5.10 A forester wants to estimate the total number of farm acres planted with trees for a state. Because the number of acres of trees varies considerably with the size of the farm, he decides to stratify on farm sizes. The 240 farms in the state are placed in one of four categories according to size. A stratified random sample of 40 farms, selected by using proportional allocation, yields the results shown in the accompanying table on number of acres planted in trees. Estimate the total number of acres of trees on farms in the state, and place a bound on the error of estimation. Graph the data on an appropriate plot and comment on the variation as we move from I to IV

5.15 Suppose in Exercise 5.13 that the total cost of sampling is fixed at $400. Choose the sample size and allocation that minimizes the variance of the estimator for this fixed cost

5.20 In Exercise 5.19, do you think stratifying on month is desirable, or would simple random sampling work just as well? Assume that taking a simple random sample is just as convenient as taking a stratified random sample.

5.25 In the use of as an estimator of m, finding an allocation and a sample size that minimizes the for fixed cost c is sometimes advantageous. That is, the cost c allowed for the survey is fixed, and we want to find the best allocation of resources in terms of maximizing the information on m. The optimum allocation in this case is still given by Eq. (5.7). Show that the appropriate choice for n is

5.30 Wage earners in a large firm are stratified into management and clerical classes, the first having 300 and the second having 500 employees. To assess attitude on sick-leave policy, independent random samples of 100 workers each were selected, one sample from each of the classes. After the sample data were collected, the responses were divided according to gender. In the table of results, a = Number who like the policy; b = Number who dislike the policy; and c = Number who have no opinion on the policy.

        Find an estimate and an estimated variance of that estimate for each parameter listed:

a.      Proportion of managers who like the policy

b.     Proportion of wage earners who like the policy

c.      Total number of female wage earners who dislike the policy

d.     Difference between the proportion of male managers who like the policy and the proportion of female managers who like the policy

e.      Difference between the proportion of managers who like the policy and the proportion of managers who dislike the policy

5.35 The U.S. Department of Agriculture records data on farm acreage and number of farms by county for every county in the country. This takes considerable time and energy, and the results for each update (usually occurring approximately every five years) are a long time in process. A quicker way to update the data is by sampling. The table below shows the number of counties in each geographic region; the farm acres (in thousands) for samples taken in the mid-1990s are available via a link from electronic Section 5.0. These are independent random samples of 22 counties from each region.

a.      Estimate the mean acreage for each region, with a margin of error.

b.     Estimate the total acreage for each region, with a margin of error.

c.      Estimate the difference between mean acreage for the North Central region and the South, with a margin of error.

d.     Estimate the difference between mean acreage for the North East and the West, with a margin of error.

e.      Estimate the mean acreage per county across the United States, with a margin of error.

5.40 In the late 1990s a sample survey of people emigrating from Cuba to Florida was conducted to obtain their opinions on conditions in their homeland. Among the 1001 sampled individuals, 87% were white and 13% were African American. It is known from census data on Cuba that the country has approximately 60% whites and 40% African Americans. One of the questions asked was

In your opinion, has the Revolution attained accomplishments in education?The accompanying table shows a summary of the responses by racial group.

a.       Assuming that the 1001 responses came from a simple random sample of emigrants, estimate the true proportion of emigrants who would answer “yes” to this question. Calculate an appropriate margin of error.

b.       Construct a poststratification estimate of the true proportion of “yes” answers among emigrants from Cuba, with an appropriate margin of error. Comment on whether or not poststratification pays any dividends in this situation.