Identify the given values.

Question

ScanSolve AI Tutor · Accepted Answer

Here's the solution for calculating the standard error of the proportion.

Identify the given values.
The total number of people surveyed is $n = 80$ .
The number of people who like the coffee brand is $x = 30$ .
Calculate the sample proportion ( $\hat{p}$ ).
$\hat{p} = \frac{x}{n} = \frac{30}{80} = 0.375$
Calculate the complement of the sample proportion ( $1 - \hat{p}$ ).
$1 - \hat{p} = 1 - 0.375 = 0.625$
Calculate the standard error of the proportion ( $SE_{\hat{p}}$ ).
The formula for the standard error of the proportion is:
$SE_{\hat{p}} = \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$
Substitute the values:
$SE_{\hat{p}} = \sqrt{\frac{0.375 \times 0.625}{80}}$ $SE_{\hat{p}} = \sqrt{\frac{0.234375}{80}}$ $SE_{\hat{p}} = \sqrt{0.0029296875}$ $SE_{\hat{p}} \approx 0.05412659$
Rounding to four decimal places, the standard error of the proportion is 0.0541.

Comparing this to the given options, the correct option is 0.0541.

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