# Out of 200 people sampled, 116 preferred Candidate A. Based on this, estimate what proportion of the voting population prefers Candidate A with 99\% confidence.

Out of 200 people sampled, 116 preferred Candidate A. Based on this, estimate what proportion of the voting population prefers Candidate A with $99\mathrm{%}$ confidence.
Out of 500 people sampled, 455 had kids.
The best point estimate for pp is.
The margin of error for a $99\mathrm{%}$ confidence interval is.
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Step 1
We need to construct the $99\mathrm{%}$ confidence interval for the population proportion.
Number of favorable cases $x=116$
Sample size $n=200$
The sample proportion is calculated as,
$\stackrel{^}{p}=\frac{x}{n}=\frac{116}{200}=0.58$
Step 2
The critical value for significance level $\alpha =0.01$ is ${z}_{c}=2.5758$
The $99\mathrm{%}$ confidence interval is computed as follows,

Therefore, the $99\mathrm{%}$ confidence interval for the population proportion is, $0.4901

0.6699$

Which indicates that we are $99\mathrm{%}$ confident that the true population proportion is contained by the intervals