# 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.