Question

we explained earlier in this lab activity that if you are not given the standard deviation of the sampling distribution, you can easily determine that standard deviation using the following the formula:

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

as an example of using the above formula, suppose we know our sample size is ( n = 50 ) and the population proportion is ( p = 0.10 ). this means the standard deviation of the sampling distribution would be:

sqrt { \frac { ( 0.10 ) ( 1 - 0.10 ) } { 50 } } = sqrt { \frac { 0.09 } { 50 } } = sqrt { 0.0018 } approx 0.0424

1 use the above formula to determine the standard deviation of a sampling distribution where the sample size is ( n = 561 ) and the population proportion is ( p = 0.29 ). show all of your work in the space below, and round your final answer to four decimal places.

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Explanation:

Step1: Substitute values into formula

Substitute \(p = 0.29\) and \(n=561\) into \(\sqrt{\frac{p(1 - p)}{n}}\).

$$ \sqrt{\frac{0.29\times(1 - 0.29)}{561}} $$

Step2: Calculate numerator

First, calculate \(1-0.29 = 0.71\), then \(0.29\times0.71=0.2059\).

$$ \sqrt{\frac{0.2059}{561}} $$

Step3: Calculate fraction

\(\frac{0.2059}{561}\approx0.000367\)

$$ \sqrt{0.000367} $$

Step4: Calculate square - root

\(\sqrt{0.000367}\approx0.0192\)

Answer:

\(0.0192\)