269 randomly selected people were surveyed to determine if they own a tablet. 150 owned a tablet....

Question:

{eq}269 {/eq} randomly selected people were surveyed to determine if they own a tablet. {eq}150 {/eq} owned a tablet. Calculate the EBP using a {eq}95\% {/eq} Confidence Level.

Margin of Error:

The margin of error gives percentage points of the true population parameter (population mean, population standard deviation, population proportion, etc). It is most likely to lie below or above the best point estimate (sample mean, sample standard deviation, sample proportion).

Answer and Explanation:

Error bound of proportion (EBP) is calculated by multiplying the critical value with the standard error:

{eq}\displaystyle EBP=Z_{\frac{\alpha}{2}}\sqrt{\frac{p(1-p)}{n}} {/eq}

Given that:

{eq}n=269\\x=150\\CL=95\% {/eq}

Find the critical value z that corresponds to a 95% level of confidence:

{eq}\displaystyle \frac{\alpha}{2}=\frac{1-0.95}{2}=0.025\\z_{0.025}=1.96 {/eq}

Calculate the best point estimate of the population proportion, the P-hat:

{eq}\begin{align*} \displaystyle EBP&=1.96\times \sqrt{\frac{0.56(1-0.56)}{269}}\\&=0.0593 \end{align*} {/eq}


Learn more about this topic:

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Finding Confidence Intervals with the Normal Distribution

from Statistics 101: Principles of Statistics

Chapter 9 / Lesson 3
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