Questions: Express the confidence interval (27.8 %, 42.8 %) in the form of p̂ ± ME.

Express the confidence interval (27.8 %, 42.8 %) in the form of p̂ ± ME.
Transcript text: Express the confidence interval $(27.8 \%, 42.8 \%)$ in the form of $\hat{p} \pm M E$.
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Solution

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Solution Steps

Step 1: Calculate the Point Estimate \(\hat{p}\)

To find the point estimate \(\hat{p}\), we calculate the midpoint of the confidence interval \((27.8\%, 42.8\%)\):

\[ \hat{p} = \frac{27.8 + 42.8}{2} = 35.3\% \]

Step 2: Calculate the Margin of Error \(ME\)

Next, we determine the margin of error \(ME\) by taking half the width of the confidence interval:

\[ ME = \frac{42.8 - 27.8}{2} = 7.5\% \]

Step 3: Express the Confidence Interval

We can now express the confidence interval in the form of \(\hat{p} \pm ME\):

\[ \hat{p} \pm ME = 35.3\% \pm 7.5\% \]

Final Answer

The confidence interval can be expressed as:

\[ \boxed{35.3 \pm 7.5} \]

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