Sampling, Estimation and Proportion
The following method was proposed to estimate the number of people over the age of 50 that reside in a town of known population 100,000. "As you walk along the streets, keep a running count of the percentage of people that you encounter who are over 50. Do this for a few days; then multiply the obtained percentage by 100,000 to obtain the estimate." Comment of this method.
Hint: Let p denote the proportion of people in this town who are over 50. Furthermore, let a1 denote the proportion of time that a person under the age of 50 spends in the streets, and let a2 be the corresponding value for those over 50. What quantity does the method suggested estimate? When is it approximately equal to p?
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Solution Preview
Let's assume that :
α1 = proportion of time that a person under 50 spends time in the streets
α2 = proportion of time that a person over 50 spends time in the streets
p = proportion of people over 50
1-p = proportion of people under 50 ...
Solution Summary
Proportions are used to make an estimate. The solution is detailed and well presented.