if 5% of people who received kidney transplants were under 18 how large a sample of patients needs to be drawn so that sample proportion of is approx. normally distributed
To determine the sample size required so that the sample proportion is approximately normally distributed, we need to consider two factors: the desired level of precision and the estimated proportion of the population.
1. Desired Level of Precision:
The desired level of precision refers to how closely the sample proportion should approximate the population proportion. This is usually expressed as a margin of error or confidence interval. Let's assume we want a margin of error of ±0.02 (2%) around the estimated population proportion.
2. Estimated Proportion of the Population:
From the given information, we know that 5% of people who received kidney transplants were under 18. This corresponds to an estimated population proportion of 0.05.
To determine the sample size, we can use the formula:
n = (z^2 * p * (1-p)) / (E^2)
where:
- n is the required sample size
- z is the z-score corresponding to the desired confidence level (usually based on the desired level of confidence, such as 95%, which corresponds to a z-score of approximately 1.96)
- p is the estimated population proportion
- E is the desired margin of error
Plugging in the values, we get:
n = (1.96^2 * 0.05 * (1 - 0.05)) / (0.02^2)
Simplifying the equation gives us the required sample size:
n ≈ (3.8416 * 0.05 * 0.95) / 0.0004
n ≈ 0.183424 / 0.0004
n ≈ 458.56
Therefore, a sample size of approximately 459 patients needs to be drawn in order to ensure that the sample proportion is approximately normally distributed, with a margin of error of ±0.02 and an estimated population proportion of 0.05.