Determine the point estimate of the population proportion.
Understand the Problem
The question is asking how to calculate the point estimate of a population proportion, which involves identifying the sample proportion from a given set of data. This typically requires using the formula for the sample proportion, which is calculated as the ratio of the number of successes to the total sample size.
Answer
The point estimate of the population proportion is $\hat{p} = 0.25$.
Answer for screen readers
The point estimate of the population proportion is $\hat{p} = 0.25$.
Steps to Solve
- Identify the number of successes and the sample size
Determine how many successes were observed in your sample and the total number of observations (sample size). For example, let’s say you have 25 successes out of a sample of 100.
- Calculate the sample proportion
Use the formula for the sample proportion, denoted as $\hat{p}$:
$$ \hat{p} = \frac{x}{n} $$
where $x$ is the number of successes and $n$ is the sample size. For our example:
$$ \hat{p} = \frac{25}{100} $$
- Evaluate the calculation
Perform the division to find the value of $\hat{p}$:
$$ \hat{p} = 0.25 $$
This means that the estimated proportion of successes in the population is 0.25, or 25%.
The point estimate of the population proportion is $\hat{p} = 0.25$.
More Information
The point estimate helps researchers understand the likelihood of a certain characteristic within a population based on sample data. In this example, it shows that approximately 25% of the sampled group exhibited the trait of interest.
Tips
- Incorrectly identifying the number of successes can lead to an inaccurate sample proportion. Ensure you count only the successes relevant to the condition being measured.
- Miscalculating the total sample size; make sure all observations are included in the denominator.
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