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# Questions about Survey Sampling

Suppose that a survey is being planned for purposes of estimating the average number of hours spent exercising daily by adults (18 years of age or older) living in a certain community. A list of all individuals living in the town is not available; however, a list of all households is available at the office of the town clerk. For simplicity, suppose this list consists of nine households and that the information you would collect, were you to visit each household, is as shown in the accompanying table.

Aggregate Number of
Household Hours Spent Exercising
1 2 1
2 3 3
3 2 7
4 5 8
5 3 4
6 1 0
7 2 1
8 3 2
9 2 0

a. Using the information above, identify:

i. The population
ii. The element of the population
iii. The sampling units
iv. The frame
v. The study (survey) variable

b. Devise a sampling plan to estimate the average daily time
expenditure on exercising by adults living in the community.

c. Select all samples of two households from this frame, and compute
the average exercising time per person for each sample.

d. Compute the expected value of your estimate, and compare this
with the actual population parameter.

#### Solution Preview

See the attached file.

Suppose that a survey is being planned for purposes of estimating the average number of hours spent exercising daily by adults (18 years of age or older) living in a certain community. A list of all individuals living in the town is not available; however, a list of all households is available at the office of the town clerk. For simplicity, suppose this list consists of nine households and that the information you would collect, were you to visit each household, is as shown in the accompanying table.

Aggregate Number of
Household Hours Spent Exercising
1 2 1
2 3 3
3 2 7
4 5 8
5 3 4
6 1 0
7 2 1
8 3 2
9 2 0

a. Using the information above, identify:

(For definitions, see ...

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