Question

In Exercises 6.1 to \(6.6,\) if random samples of the given size are drawn from a population with the given proportion, find the standard error of the distribution of sample proportions. Samples of size 100 from a population with proportion 0.41

Short answer

The standard error of the distribution of sample proportions is \( 0.049 \).

Step-by-step solution

Identify Given Values

First, identify the given values from the problem statement. The sample size \( n \) is 100 and the population proportion \( p \) is 0.41.

Insert values into formula

Next, insert these values into the formula for the standard error of the distribution of sample proportions. Which would be \( \sqrt{ \frac{ 0.41(1-0.41) }{ 100 } } \)

Evaluate the expression

Evaluate the expression \( \sqrt{ \frac{ 0.41(0.59) }{ 100 } } \) using calculation or a calculator to find the standard error.