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Chapter 7: Q10 (page 311)

Formats of Confidence Intervals.

In Exercises 9鈥�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 鈥淢&M Weights鈥� in Appendix B.)

Orange M&Ms Express 0.179 < p < 0.321 in the form of p^卤E.

Short Answer

Expert verified

The confidence interval of the format p^卤Eis0.25卤0.071.

Step by step solution

01

Given information

The confidence interval for p is0.179<p<0.321

02

Find the value of sample proportion

Formula for sample proportion is:

p^=upper confidence limit+lower confidence limit2

From the given confidence interval, thelower confidence limit is 0.179 and upper confidence limit is 0.321.

Substituting values,

p^=0.321+0.1792=0.25

Hence, the sample proportion is 0.25.

03

Find the value of margin of error

Formula for margin of error is:

E=upper confidence limit-lower confidence limit2=0.321-0.1792=0.071

Hence, the margin of error is 0.071.

04

Construct the confidence interval in the form of p^ ± E

The confidence interval in the form of p^卤Eis given as:

p^-E<p<p^+E0.25-0.071<p<0.25+0.0710.179<p<0.321

Therefore, the confidence interval in the format p^卤Eis 0.25卤0.071.

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Formats of Confidence Intervals.

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