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Chapter 7: Q9 (page 311)

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.)

Red M&Ms Express 0.0434 < p < 0.217 in the form ofp+E

Short Answer

Expert verified

The confidence interval in the form of p^±Eis0.130±0.087

Step by step solution

01

Given information

The confidence interval for p is0.0434<p<0.217

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 0.0434 and the upper confidence limit is 0.217.

Substituting values,

p^=0.217+0.04342=0.1302

Hence, the sample proportion is 0.130.

03

Find the value of margin of error

Formula for margin of error is:

E=upper confidence limit-lower confidence limit2=0.217-0.04342=0.0868

Hence, the margin of error is 0.087.

04

Construct the confidence interval in the form of p±E

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

p^-E<p<p^+E0.1302-0.0868<p<0.1302+0.08680.0434<p<0.217

Therefore, the confidence interval in the form of p^±Eis 0.1302±0.0868.

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