SOLUTION: A simple random sample of 1600 persons is taken to estimate the percentage of Democrats among 25000 eligible voters in a certain town. It turns out that 852 people in the sample ar

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Question 1148744: A simple random sample of 1600 persons is taken to estimate the percentage of Democrats among 25000 eligible voters in a certain town. It turns out that 852 people in the sample are Democrats.
We can be 95 percent confident that between __ percent and ___ percent of the voters are Democrats.
Answer by VFBundy(438) About Me  (Show Source):
You can put this solution on YOUR website!
If 852 people out of 1600 people in the sample are Democrats, that means 53.25% of people in the sample are Democrats. So, the mean is 0.5325.

To find the standard deviation of the sample, use the formula: sqrt%28%28p%281-p%29%29%2Fn%29

sqrt%28%280.5325%281-0.5325%29%29%2F1600%29 = sqrt%28%280.5325%280.4675%29%29%2F1600%29 = sqrt%28%280.2489%29%2F1600%29 = 0.0125

To find a 95% confidence interval, we need to find the area under the curve that is between 97.5% and 2.5%. Go to a z-table and find the z-scores that correspond to these values. You will find that the z-scores that correspond to this are +1.96 and -1.96.

So, we know the mean of the sample is 0.5325, we know the the standard deviation of the sample is 0.0125, and we are looking for the area under the curve that is between 1.96 and -1.96 standard deviations. To find the confidence interval, we set up the following equations:

0.5325 + 1.96(0.0125) = 0.557
0.5325 - 1.96(0.0125) = 0.508

So, we can be 95% confident that between 50.8% and 55.7% of the voters are Democrat.