To calculate the point estimate (\(X\)) using the Wilson Estimation:
\[ X = \frac{S + z^2/2}{T + z^2} \]
Where:
A point estimate is a single value that is used to estimate an unknown parameter of a population based on sample data. It provides an approximation of the true value of the parameter of interest.
Point estimates are crucial as they allow researchers to make inferences about the entire population using only a sample. They represent the population’s characteristics, providing a glimpse into the unknown. By calculating a point estimate, researchers can gain insights about a population without collecting data from every individual.
Point estimates play a pivotal role in decision-making processes. They are used to estimate parameters such as population means, proportions, or variances. For example, if a company wants to estimate the average age of its customers, a point estimate can be calculated using a sample of the customers’ ages. This estimate can then be used to guide marketing strategies, product development, or customer service initiatives.
Let's assume the following values:
Using the formula:
\[ X = \frac{50 + 1.96^2/2}{100 + 1.96^2} = \frac{50 + 1.9208}{100 + 3.8416} = \frac{51.9208}{103.8416} = 0.4999 \]
The point estimate is 0.4999.
Let's assume the following values:
Using the formula:
\[ X = \frac{30 + 1.64^2/2}{80 + 1.64^2} = \frac{30 + 1.3448}{80 + 2.6896} = \frac{31.3448}{82.6896} = 0.3792 \]
The point estimate is 0.3792.