# Exercises and Discussion Questions

3.1       Take a class roster – or any list – and draw a simple random sample and a systematic sample from it.

There is no set answer to this question. Just follow the procedures given in Section 3.1.

3.2       In a survey on parks and recreation, 40% of respondents are under 55 years of age, and 60% are 55 and over. The relevant population is known to have 80% under 55 and 20% over. The unweighted survey results indicate that 26% of area residents want more children’s playgrounds in city parks: 50% for respondents under 55 years of age and 10% for respondents 55 and over. If these results are weighted to correct for age, what percentage of area residents want more children’s playgrounds?

The unweighted result, given in the exercise, is 26% [(50% * .4) + (10% * .6)]. If (a) 50% of respondents younger than 55 years favor more playgrounds, and those respondents are 40% (or .4) of the sample, and (b) 10% of respondents 55 years or older favor more playgrounds, and those respondents are 60% (or .6) of the sample, then (c) 50% of .4 of the sample plus 10% of .6 of the sample equals 26% of the entire sample.

The weighted result is 42% [(50% * .8) + (10% * .2)]. People younger than 55 years are 40% (or .4) of the sample, but they are 80% (or .8) of the population. Similarly, people 55 years or older are 60% (or .6) of the sample, but they are only 20% (or .2) of the population. If 50% of people younger than 55 years favor more playgrounds, and those respondents are 80% (or .8) of the population, and (b) 10% of respondents 55 years or older favor more playgrounds, and those respondents are 20% (or .2) of the population, then (c) 50% of .8 of the population plus 10% of .2 of the population equals 42% of the entire population.

The 26% unweighted result reflects the obtained sample, which overrepresents older people and underrepresents younger people. The 42% weighted result reflects the population’s age composition.