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.)

Yellow M&Ms Express the confidence interval (0.0169, 0.143) in the form of$\hat{p}-E<p<\hat{p}+E$

Short answer

The confidence interval is expressed as$0.0169<p<0.143$.

Step-by-step solution

Given information

The confidence interval for the proportion of yellow M&Ms has an upper confidence limit equal to 0.143 and a lower confidence limit equal to 0.0169.

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 lower limit of the confidence interval is equivalent to $\hat{p}-E$while the upper limit of the confidence interval is equivalent to $\hat{p}+E$.

Therefore, the lower limit of the given confidence interval (0.0169) is equivalent to $\hat{p}-E$and the upper limit (0.143) is equivalent to $\hat{p}+E$.

The expression of the confidence interval of the proportion of yellow M&Ms is equal to$0.0169<p<0.143$.