### Poll Analysis and Confidence IntervalsA poll is taken in which **363 out of 575** randomly selected voters indicated their preference for a certain candidate.#### (a) 95% Confidence Interval Calculation- Find a 95% confidence interval for \( p \).\[ \text{Enter lower bound} \leq p \leq \text{Enter upper bound} \]#### (b) Margin of Error Determination- Find the margin of error for this 95% confidence interval for \( p \).\[ \text{Enter margin of error} \]#### (c) Margin of Error Comparison- Without doing any calculations, indicate whether the margin of error is larger or smaller or the same for an 80% confidence interval. - **A.** larger - **B.** smaller - **C.** sameUse this information to understand how confidence intervals are constructed and how margins of error change with different confidence levels.

(a) A pool is taken in which 363 out of 575 randomly selected voters indicated their performance for a certain candidate. That is, n=575,p=363. The sample proportion is, p^=xn=363575=0.6313 The confidence level is 95%. Computation of critical value: 1-α=0.95α=0.05α2=0.0251-α2=0.975 The critical value of z-distribution can be obtained using the excel formula “=NORM.S.INV(0.975)”. The critical value is 1.96. The 95% confidence interval for p is, p^+zα2p^1-p^n≤p≤p^+zα2p^1-p^n0.6313-1.960.63131-0.6313575≤p≤0.6313+1.960.63131-0.63135750.6313-0.0394≤p≤0.6313+0.03940.5919≤p≤0.6707 Thus, the 95% confidence interval for p is 0.5919≤p≤0.6707.(b) The margin of error for this 955 confidence interval for p is, E=zα2p^1-p^n=1.960.63131-0.6313575=0.0394 Thus, the margin of error for this 955 confidence interval for p is 0.0394. (c) When the confidence interval decreases to 80% from 95% , then the margin of error is smaller because the critical value would decreased. Thus, the margin of error is smaller for an 80% confidence interval.

Answered: A poll is taken in which 363 out of 575…

Math

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A poll is taken in which 363 out of 575 randomly selected voters indicated their preference for a certain candidate. (a) Find a 95% confidence interval for р.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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