To estimate the variation among sample proportions, we need to compute the standard deviation of the sampling distribution of the sample proportion, which is known as the standard error of the proportion.

The formula for the standard error of a sample proportion is:

$SE = \sqrt{\frac{p(1 - p)}{n}}$

Where:

• $p$ is the population proportion (given as 0.43),
• $n$ is the sample size (given as 50).

Now, let's substitute the values into the formula:

$SE = \sqrt{\frac{0.43(1 - 0.43)}{50}}$ $SE = \sqrt{\frac{0.43(0.57)}{50}}$ $SE = \sqrt{\frac{0.2451}{50}}$ $SE = \sqrt{0.004902}$ $SE \approx 0.070$

Thus, the standard error of the proportion for a sample size of 50 is approximately 0.070.

Summary:

The variation among sample proportions (standard error) for samples of size 50 is approximately 0.070.

Would you like more details on this calculation or have any further questions? Here are some related questions:

1. How would the standard error change if the sample size increased to 100?
2. What is the difference between standard error and standard deviation in this context?
3. What happens to the sample proportion if the true population proportion were different, say 0.5?
4. How can we use the standard error to calculate confidence intervals for the proportion?
5. What are the assumptions we make when calculating the standard error for proportions?

Tip: Increasing the sample size reduces the standard error, leading to more precise estimates of the population proportion.