Express the confidence interval 79%<p<91.6% in the form of p^±ME.

% ± %

To express the confidence interval \( 79\% < p < 91.6\% \) in the form \( \hat{p} \pm ME \), we first need to find the midpoint (\(\hat{p}\)) and the margin of error (ME).

1. **Calculate the midpoint \(\hat{p}\)**:
   \[
   \hat{p} = \frac{79\% + 91.6\%}{2} = \frac{170.6\%}{2} = 85.3\%
   \]

2. **Calculate the margin of error (ME)**:
   \[
   ME = \frac{91.6\% - 79\%}{2} = \frac{12.6\%}{2} = 6.3\%
   \]

Now, we can express the confidence interval as:
\[
\hat{p} \pm ME = 85.3\% \pm 6.3\%
\]

Thus, the confidence interval can be written as:
\[
85.3\% \pm 6.3\%
\]

If you have any questions or need further details, let me know! Here are some related questions you might consider:

1. What does the confidence level represent in a statistical context?
2. How do you interpret the margin of error in practical terms?
3. What factors can affect the width of a confidence interval?
4. How do you calculate confidence intervals for different confidence levels?
5. Can you explain the difference between a point estimate and a confidence interval? 

**Tip:** Always check the assumptions for the sample data when calculating confidence intervals to ensure the results are valid.

Express the confidence interval 79% < p < 91.6% in the form of p^±ME.

Learn how to express the confidence interval 79% < p < 91.6% in the form of p^±ME. This solution includes step-by-step calculations for the midpoint and margin of error, suitable for high school students.

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