Question

Formats of Confidence Intervals. In Exercises 9–12, 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 27 “M&M Weights” in Appendix B.)

Blue M&Ms Express the confidence interval 0.270\( \pm \)0.073 in the form of\(\hat p - E < p < \hat p + E\)

Short answer

The confidence interval is expressed as \(0.197 < p < 0.343\).

Step-by-step solution

Given information

The confidence interval for the proportion of blue M&Ms is given as 0.270 \( \pm \)0.073.

Expression of the confidence interval

The confidence interval for the population proportion can be expressed as follows:

\(\hat p - E < p < \hat p + E\)

The value written before the plus-minus sign is regarded as the sample proportion\(\left( {\hat p} \right)\)while the value written after the plus-minus sign is regarded as the margin of error (E).

Thus, the value of\(\hat p - E\)is computed below:

\(\begin{array}{c}\hat p - E = 0.27 - 0.073\\ = 0.197\end{array}\)

The value of\(\hat p - E\)is computed below:

\(\begin{array}{c}\hat p + E = 0.27 + 0.073\\ = 0.343\end{array}\)

Therefore, the expression of the confidence interval of the proportion of blue M&Ms is equal to \(0.197 < p < 0.343\).