7.2
Sample Proportion and Population Proportion
In a global survey, a researcher found that 8500 out of 10,000 respondents suggested legally protecting the rain forest.
It is impossible to receive responses from everyone in the global population. So, these 10,000 responses can be utilized for analysis, what is called a sample, drawn from the population.
The ratio 8500 divided by 10,000—the proportion of people suggesting legal protection of rainforests—gives us a value 0.85, or 85%, which is called a sample proportion, denoted as 
.
Assuming that the sample of 10,000 individuals accurately represents the whole population, the sample proportion can be used to estimate the population proportion, denoted as 
.
The single value obtained from such a sample is then called the point estimate. In this case, the sample proportion 0.85, or 85% is the point estimate of the population proportion.
Multiple such sample proportions can be obtained by conducting the survey repeatedly to determine if a point estimate is unbiased. It is considered unbiased when the standard deviation around it is small.
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.
In a global survey, a researcher found that 8500 out of 10,000 respondents suggested legally protecting the rain forest.
It is impossible to receive responses from everyone in the global population. So, these 10,000 responses can be utilized for analysis, what is called a sample, drawn from the population.
The ratio 8500 divided by 10,000—the proportion of people suggesting legal protection of rainforests—gives us a value 0.85, or 85%, which is called a sample proportion, denoted as .
Assuming that the sample of 10,000 individuals accurately represents the whole population, the sample proportion can be used to estimate the population proportion, denoted as .
The single value obtained from such a sample is then called the point estimate. In this case, the sample proportion 0.85, or 85% is the point estimate of the population proportion.
Multiple such sample proportions can be obtained by conducting the survey repeatedly to determine if a point estimate is unbiased. It is considered unbiased when the standard deviation around it is small.
From Chapter 7:
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7.2 : Sample Proportion and Population Proportion
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7.1 : What are Estimates?
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7.3 : Confidence Intervals
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7.4 : Confidence Coefficient
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7.5 : Interpretation of Confidence Intervals
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7.6 : Critical Values
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7.7 : Margin of Error
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7.8 : Sample Size Calculation
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7.9 : Estimating Population Mean with Known Standard Deviation
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7.10 : Estimating Population Mean with Unknown Standard Deviation
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7.11 : Confidence Interval for Estimating Population Mean
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