Question

Consider random samples of size 800 from a population with proportion 0.65 . Find the standard error of the distribution of sample proportions.

Round your answer for the standard error to three decimal places.
Standard error =________

Answer 1

To calculate the standard error of the distribution of sample proportions for a population proportion of 0.65 and a sample size of 800, the formula SE = √(p(1 - p)/n) is used, yielding a standard error of 0.017 when rounded to three decimal places.

Step-by-step explanation:

To find the standard error of the distribution of sample proportions, we can use the formula for the standard error of a proportion:

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

where p is the population proportion, and n is the sample size. Plugging in the given values, we have:

SE = \( \sqrt{\frac{0.65(1 - 0.65)}{800}} \)

Performing the calculation:

SE = \( \sqrt{\frac{0.65 \times 0.35}{800}} \) = \sqrt{\frac{0.2275}{800}} = \sqrt{0.000284375} \approx 0.017

Therefore, the standard error, rounded to three decimal places, is 0.017.