what are the mean and standard error when using central limit theorem for dichotomous variable

To calculate the mean and standard error when using the Central Limit Theorem for a dichotomous variable, follow these steps:

Step 1: Determine the sample size (n) and the proportion of the event of interest (p) in the population.

Step 2: Calculate the mean (μ) by multiplying the sample size (n) by the proportion (p): μ = n * p.

Step 3: Calculate the standard error (SE) using the formula: SE = √(p * (1 - p) / n).

Let's break down each step further:

Step 1: Determine the sample size (n) and the proportion of the event of interest (p) in the population.

Sample Size (n): This refers to the number of observations or data points in your sample. It should be random and representative of the population.

Proportion (p): This is the likelihood or probability of the event of interest occurring within the dichotomous variable. It can be expressed as a decimal or a percentage.

Step 2: Calculate the mean (μ) by multiplying the sample size (n) by the proportion (p): μ = n * p.

The mean (μ) of a dichotomous variable in this context represents the expected value or average frequency of the event of interest occurring within the sample. It is obtained by multiplying the sample size (n) by the proportion (p) of the event occurring.

Step 3: Calculate the standard error (SE) using the formula: SE = √(p * (1 - p) / n).

The standard error (SE) is a measure of the variation or uncertainty in the sample mean. It represents the average deviation of the sample means from the population mean. It is calculated by taking the square root of the product of p * (1 - p) divided by the sample size (n).

By following these steps, you can calculate the mean and standard error for a dichotomous variable using the Central Limit Theorem.