Confidence Intervals
Examples of True Proportion (p) Estimation
Learning Objectives
In this section, we will examine applications of estimating true population proportions.
As introduced earlier, there are many important industry/business situations where we may be interested in estimating the true proportion of a population (i.e., symbolically represented using [latex]\pi[/latex] or [latex]p[/latex]). Recall that a proportion is simply a fraction or a percentage of a population.
Polling
For example, one of the most common situations where we all hear about the estimation of a population proportion is during various polls. Polls are surveys that are designed to elicit information or opinions about a particular topic from populations. Almost every day, the media publishes information regarding the results of some poll being conducted. For example, the following was recently published in a Canadian newspaper:
(Angus Reid Global Monitor) - According to the survey released late Thursday, if an election were held tomorrow, 34 per cent of us would vote for the Conservatives, 30 per cent would vote for the NDP, and 26 per cent would for the federal Liberals.
Activity Sampling
Estimating the proportion of a population also relates to Activity Sampling. Activity Sampling is
- a technique in which a large number of observations are made over a period of time of one group of machines, processes or workers.
- Each observation is a record of what is happening at that instant and the percentage of observations recorded for a particular activity or delay is a measure of the percentage of time during which that activity or delay occurs.
- It is normally used for collecting information on the percentages of time spent on activities, without the need to devote the time that would otherwise be required for any continuous observation.
One of the great advantages of this technique is that it enables lengthy activities or groups of activities to be studied economically and in a way that produces statistically accurate data.
Marketing Research
A third important area where proportions are important is in marketing:
- Responses to new feature on a website
- Percent of company’s budget allocated to marketing
- Click-through rates on advertisements
- Conversion rates
- Percent of total ad spend allocated to mobile advertising
- Search engine optimization statistics
