Binomial Test Sample Size Calculator

Calculate Sample Size (n)



Formula

The formula to calculate the Sample Size (n) is:

\[ n = \frac{k}{p} \]

Where:

Definition

Example

Let's say the number of successes (k) is 30 and the success probability (p) is 0.6. Using the formula:

\[ n = \frac{30}{0.6} = 50 \]

So, the Sample Size (n) is 50.

Extended information about "Binomial-Test-Sample-Size-Calculator"

One Sample Binomial Test

Definition: A statistical test used to determine if the proportion of successes in a sample is significantly different from a hypothesized proportion.

Formula: \( P = \frac{k!}{x!(k-x)!} p^x (1-p)^{k-x} \)

Example: \( P = \frac{10!}{3!(10-3)!} 0.5^3 (1-0.5)^{10-3} \)

Binomial Distribution Sample Size

Definition: The sample size required for a binomial distribution to achieve a desired level of accuracy.

Formula: \( n = \frac{Z^2 p (1-p)}{E^2} \)

Example: \( n = \frac{1.96^2 \times 0.5 \times (1-0.5)}{0.05^2} \)

Negative Binomial Sample Size Calculation

Definition: The sample size required for a negative binomial distribution to achieve a desired level of accuracy.

Formula: \( n = \frac{Z^2 p (1-p)}{E^2} \)

Example: \( n = \frac{2.58^2 \times 0.3 \times (1-0.3)}{0.1^2} \)