7.2 : Sample Proportion and Population Proportion

Collecting samples or responses from an entire population takes significant time and effort, so a researcher collects responses from only a sample of that population. Suppose a study needs to collect information about a specific mobile application. After sample collection, the researcher analyzes the data and discovers that most individuals in the sample use that specific mobile application. The sample proportion measures the number of individuals in a sample who either use or don't use the mobile application. This sample proportion, a single value, is a representative measure of the population proportion and is called a point estimate.

For example, a researcher collects 10,000 sample responses about a specific mobile application. After collection, it was observed that 9000 individuals used the mobile application. From this information, the researcher can calculate the sample proportion of the individuals using the application by dividing 9000 by the total number of responses, 10000, to get a value of 0.90. This value can be expressed as a percentage of 90%.

Furthermore, a sample proportion can be calculated from multiple samples of the population to ensure that the point estimate is unbiased. If the standard deviation among the sample proportions is small, then the point estimate is considered unbiased.