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:

$$\begin{gathered} \hat{p}-E=0.27-0.073 \\ =0.197 \end{gathered}$$

The value of $\hat{p}-E$is computed below:

$$\begin{gathered} \hat{p}+E=0.27+0.073 \\ =0.343 \end{gathered}$$

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