1. A simple random sample of 30 households (hhs) was drawn from a city area containing 14,848 hhs. The number of persons per hh in the sample were as follows:

5, 6, 3, 3, 2, 3, 3, 3, 4, 4, 3, 2, 7, 4, 3, 5, 4, 4, 3, 3, 4, 3, 3, 1, 2, 4, 3, 4, 2, 4

Estimate the total number of people in the area and compute the probability that this estimate is within ±10% of the true value.

2. In a study of the possible use of sampling to cut down the work in taking inventory in a stock room, a count is made of the value of the articles on each of 36 shelves in the room. The values to the nearest peso are as follows:

29, 38, 42, 44, 45, 47, 51, 53, 53, 54, 56, 56, 56, 58, 58, 59, 60, 60, 60, 60
61, 61, 61, 62, 64, 65, 65, 67, 67, 68, 69, 71, 74, 77, 82, 85

The estimate of total value made from a sample is to be corrected within P200, apart from a 1 in 20 chance. An advisor suggests that a simple random sample of 12 shelves will meet the requirements. Do you agree?

3. From a list of 468 small two-year colleges, a simple random sample of 100 colleges was drawn. The sample contained 54 public and 46 private colleges. Data for number of students (y) and number of teachers (x) are shown below:

n ∑ (y) ∑ (x) ∑ (y2) ∑ (yx) ∑ (x2)
Public 54 31,281 2,024 29,881,219 1,72...
Private 46 13,707 1,075 6,366,785 431,...

a. For each type of college in the population, estimate the ratio (number of students)/(number of teachers).

b. Compute the standard errors of your estimates.

c. For the public colleges, find 90% confidence units for the student/teacher ratio in the whole population.

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