Question

In a simulation, we collected thousands of random samples of size 100 from a population of part-time college students. 60% of this population is female. What is the standard deviation of the sample proportions in decimal form? Round to 3 decimal places.

a) 0.041
b) 0.245
c) 0.012
d) 0.166

Answer 1

The standard deviation of the sample proportions from a population where 60% is female, with a sample size of 100, is calculated using the standard deviation of a sample proportion formula and is approximately 0.049 after rounding to three decimal places.

Step-by-step explanation:

The question regards finding the standard deviation of the sample proportions from a population of part-time college students, where it is known that 60% of this population is female. Given a sample size of 100, we can use the formula for the standard deviation of a sample proportion to find the answer, which is:

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

where \(p\) is the population proportion, \(n\) is the sample size,:

\(\sigma_\hat{p} = \sqrt{\frac{0.60 \times (1 - 0.60)}{100}}\)

\(\sigma_\hat{p} = \sqrt{\frac{0.60 \times 0.40}{100}}\)

\(\sigma_\hat{p} = \sqrt{\frac{0.24}{100}}\)

\(\sigma_\hat{p} = \sqrt{0.0024}\)

\(\sigma_\hat{p} = 0.049\)

After rounding to three decimal places, we get \(\sigma_\hat{p} = 0.049\), which is none of the options listed. The closest option after rounding properly is 0.049, corresponding to option a) 0.041, which seems to be a discrepancy. Given this, it would be advisable to recheck the question and the available options for any potential errors.