Calculate 95% Confidence Interval in Public Opinion Polls

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In summary, when conducting a public opinion poll, the binomial approximation can be used to calculate a 95% confidence interval, but to make inferences about the total population, the hypergeometric distribution must be used.
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Lobotomy
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hello
when doing a public opinion poll before an election in a country, they usually approximate the hypergeometric distribution with a binomial distribution and then using the normal approximation:

m +/-1.96*sqrt(m*(1-m)/n) to calculate a 95% confidence interval?
m= mean
n= number of people in the poll

is it as simple as that? assuming party A gets 30% of the votes, and 2000 voted we get a 95% statistically significant interval of:
30 +/-1.96*sqrt(0.30*(0.7)/2000)

is it as simple as that? i think this is what i learned in school a long time ago...

However if we make a poll within a defined population of let's say 5000 people. and the number of people in the poll is 3000. party A gets 30% of the votes in the poll. What can we say about the total population of 5000.
here we should use the hypergeometric distribution and can not use the binomialapproximation. I've only used the hypergeometric distribution in examples of sampling without replacement, where we want to calculate the probability of drawing a certain color ball. However this time, we draw som balls and we want to say something about the pot itself right (the balls are the votes and the pot is the total population vote). How do we do this?
 
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Yes, you are correct in that the binomial approximation can be used to calculate the 95% confidence interval with the given parameters. However, in order to make an inference about the total population of 5000 people, you will need to use the hypergeometric distribution as you noted. The hypergeometric distribution is a probability distribution that describes the number of successes in a sample of size n from a population of size N, where each member of the population has a different probability of being chosen. In this case, the population size is 5000 and the sample size is 3000. The number of "successes" is 30%, which is the proportion of votes for party A. Using the hypergeometric distribution, you can then calculate the probability of obtaining a certain number of successes in the sample, given the population size and number of successes in the population. From this, you can make inferences about the total population of 5000 people.
 

1. How is the 95% confidence interval calculated in public opinion polls?

The 95% confidence interval in public opinion polls is calculated by taking the sample size, margin of error, and confidence level into account. First, the pollster collects a random sample of individuals from the population of interest. Then, using statistical formulas, they calculate the margin of error, which takes into account the sample size and confidence level. Finally, the 95% confidence interval is calculated by adding and subtracting the margin of error from the sample's mean.

2. What does a 95% confidence interval mean in public opinion polls?

A 95% confidence interval in public opinion polls means that if the same survey were to be conducted multiple times, 95% of the time, the true population parameter (such as the proportion of people who support a particular candidate) would fall within the calculated interval. In other words, there is a 95% chance that the survey results accurately reflect the opinions of the entire population being studied.

3. Why is a 95% confidence interval commonly used in public opinion polls?

A 95% confidence interval is commonly used in public opinion polls because it provides a balance between precision and reliability. It is a narrow enough range to give a specific estimate of the population parameter, but also wide enough to account for any potential sampling errors. Additionally, a 95% confidence interval is a standard in the field of statistics and is widely recognized and accepted by researchers and the general public alike.

4. How does the sample size affect the width of the 95% confidence interval in public opinion polls?

The sample size has a direct impact on the width of the 95% confidence interval in public opinion polls. A larger sample size will result in a smaller margin of error, which in turn will lead to a narrower confidence interval. This is because a larger sample size provides a more accurate representation of the population, reducing the potential for sampling errors. Conversely, a smaller sample size will result in a larger margin of error and a wider confidence interval.

5. Are there any limitations to using a 95% confidence interval in public opinion polls?

Yes, there are some limitations to using a 95% confidence interval in public opinion polls. First, the margin of error and confidence interval calculations assume that the sample was selected randomly and is representative of the entire population. If the sample is not truly random or is biased in some way, the results may not accurately reflect the opinions of the entire population. Additionally, the margin of error and confidence interval do not account for non-sampling errors, such as response bias or measurement error, which can also affect the accuracy of the results.

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