Express the confidence interval using the indicated format....

Express the confidence interval using the indicated format. (The confidence intervals are based on the proportions of red, orange, yellow, and blue M&Ms in Data Set 20 from Appendix B.)
Express the confidence interval (0.0268,0.133) in the form of $p^{\wedge}-E<p<p^{\wedge}+E$.

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Key Concepts

Margin of Error

The margin of error represents the maximum expected difference between the point estimate and the true population parameter. It is calculated as half the width of the confidence interval, and it quantifies the uncertainty in the estimate, providing a range within which the true parameter value is expected to lie.

Confidence Interval

A confidence interval is a range of values derived from sample data that is likely to contain the true value of an unknown population parameter. It is constructed so that a specified proportion (the confidence level) of such intervals will contain the parameter, offering a measure of estimation precision under uncertainty.

Point Estimate

The point estimate is the single best estimate of a population parameter, commonly calculated as the midpoint of a symmetric confidence interval. In the context of the confidence interval format p? ± E, the point estimate p? is the center of the interval and serves as the basis for constructing the margin of error.

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