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1) A certain pollster company finds in a survey of 30 voters that a presidential candidate is favored to win with 51% of the votes. Construct a 99% confidence interval for the true proportion of all voters in favor of the candidate. $n = 30$ $p = 0.51$ $0.51 \pm 2.576 \times 0.0913$ $0.51 \pm 0.2352$ $[0.2748, 0.7452]$ [0.27, 0.75]$ we are 99% confident that the true proportion of all voters in favor of the candidate is between 0.27 and 0.75. 2) If the pollster from problem 1 wanted to construct a 99% confidence interval showing her candidate is favored by a majority, how many people should she survey?

          1) A certain pollster company finds in a survey of 30 voters that a presidential candidate is favored to win
with 51% of the votes. Construct a 99% confidence interval for the true proportion of all voters in favor
of the candidate. $n = 30$ $p = 0.51$
$0.51 \pm 2.576 \times 0.0913$
$0.51 \pm 0.2352$
$[0.2748, 0.7452]$
[0.27, 0.75]$
we are 99% confident that the true proportion
of all voters in favor of the candidate is
between 0.27 and 0.75.
2) If the pollster from problem 1 wanted to construct a 99% confidence interval showing her candidate is
favored by a majority, how many people should she survey?
        
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1) A certain pollster company finds in a survey of 30 voters that a presidential candidate is favored to win
with 51% of the votes. Construct a 99% confidence interval for the true proportion of all voters in favor
of the candidate. n = 30 p = 0.51
0.51 ± 2.576 × 0.0913
0.51 ± 0.2352
[0.2748, 0.7452]
[0.27, 0.75]we are 99% confident that the true proportion
of all voters in favor of the candidate is
between 0.27 and 0.75.
2) If the pollster from problem 1 wanted to construct a 99% confidence interval showing her candidate is
favored by a majority, how many people should she survey?

Added by Brian G.

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Elementary Statistics a Step by Step Approach
Elementary Statistics a Step by Step Approach
Allan G. Bluman 9th Edition
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A certain polling company finds in a survey of 30 voters that a presidential candidate is favored to win with 51% of the votes. Construct a 99% confidence interval for the true proportion of all voters in favor of the candidate. n = 30, p̂ = 0.51, q̂ = 0.49, α = 0.01, z = 2.576. The confidence interval is between 0.27 and 0.70. The margin of error is 0.013. The lower limit of the confidence interval is 0.510255 and the upper limit is 0.689745.
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Transcript

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00:01 Alright, so in the given question, we have been asked to construct the 99 % confidence interval for the population proportion.
00:09 So here the size of the sample is 180 with number of favorable outcomes as 36.
00:14 So the point estimate or sample proportion will be x divided by n, that is 36 divided by 180, which is equal to 0 .2.
00:24 Now here, the confidence level is 99%.
00:28 So alpha will be 1 minus 0 .99.
00:31 That is 0 .01 and for alpha 0 .01 the critical value will be 2 .576 right now sorry so here the formula to construct the confidence interval this is equal to sample proportion plus minus the critical value multiplied by standard errors this is the formula for standard error right we put all the values in there this is 0 .2 plus minus 2 .576 multiplied by square root of 0 .2 into 1 minus 0 .2 divided by 180...
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