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Chapter 7: Q10 (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.)

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

Short Answer

Expert verified

The confidence interval of the format p^±Eis0.25±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^±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^±Eis 0.25±0.071.

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Most popular questions from this chapter

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0 0 34 34 34 45 41 51 55 36 47 41 0 0 53 54 38 0 41 47
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