Question

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.) Express $0.179<p<0.321$ in the form of $\hat{p} \pm E$.

Name: Problem 10, Chapter 7: Elementary Statistics
Uploaded: 2020-11-02T06:58:54-08:00
Duration: 1 min 1 s
Channel: Harsh Gadhiya
Description: 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.) Express 0.179<p<0.321 in the form of p̂ ±E.

   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.)
Express $0.179<p<0.321$ in the form of $\hat{p} \pm E$.

Elementary Statistics

Mario F. Triola 13th Edition

Chapter 7, Problem 10

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Solved by Expert Harsh Gadhiya

11/02/2020

Step 1

This is given by the average of the lower limit and the upper limit of the confidence interval. Mathematically, this can be expressed as: \[\hat{p} = \frac{{\text{{lower limit}} + \text{{upper limit}}}}{2}\] Substituting the given values into the equation, we Show more…

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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.) Express $0.179<p<0.321$ in the form of $\hat{p} \pm E$.

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Key Concepts

Confidence Interval

A confidence interval is a range of values used to estimate an unknown population parameter. It provides a measure of uncertainty about the estimate by presenting an upper and lower bound, indicating that the true parameter is likely to lie within this interval with a specified level of confidence.

Point Estimate

The point estimate is a single value that acts as the best estimate of the population parameter. In the context of a confidence interval expressed in the form p? ± E, the point estimate is usually the midpoint of the interval, reflecting the center around which the parameter is estimated.

Margin of Error

The margin of error represents the maximum expected difference between the point estimate and the true value of the parameter. It quantifies the uncertainty of the estimate and is calculated as half the width of the confidence interval, providing the amount that is added to and subtracted from the point estimate in the p? ± E format.

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