Question

A poll is taken in which 365365 out of 575575 randomly selected voters indicated their preference for a certain candidate.

(a) Find a 9595% confidence interval for pp.

≤p≤≤p≤

(b) Find the margin of error for this 9595% confidence interval for pp.



(c) 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. same

Answer 1

Sample proportion ($\small \hat{p}$) = 0.6348
Sample size (n) = 575
Confidence interval(in %) = 95
z @ 95% = 1.96
a) Since we know that

p(1-P) Confidence interval = pt av 0.6348(1 -0.6348) 0.6348 + Required confidence interval = (0.6348 – 1.961 1.96 0.6348(1 – 0.6348)

Required confidence interval = (0.6348-0.0394, 0.6348+0.0394)
Required confidence interval = (0.5954, 0.6742)

p(1-P) b)Margin of error = *a 0.6348(1-0.6348) Margin of error = 1.96 575 Margin of error = 0.0394

c) B. smaller, because as confidence decreases, z value also decreases which in turn result in a smaller margin of error

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