# generating a 95% confidence interval.

**statistics**

Sample statistics, such as the sample mean or the sample proportion, can be used to estimate a population parameter (such as the population mean or the population proportion). For example, you can estimate the true mean weight of all newborn babies in the entire world by collecting a sample and using that sample to generate a 95% confidence interval.

Because the sample is a relatively little portion of the entire population, errors will have to be considered. Using a sample to create a range or interval of values that estimates a population value is called a “confidence interval.”

The formula for calculating a 95% confidence interval for a population mean is:

The general “Confidence Interval” formula is:

sample mean – E < population mean < sample mean + E

To calculate a confidence interval, the margin of error (E) must first be calculated.

The Margin of Error, E, for means is: E = 1.96*s/sqrt(n), where s is the sample standard deviation, n is the sample size. The “sqrt” stands for square root.

The Margin of Error, E, for proportions is: E = 1.96*sqrt[p*(1-p)/n], where s is the sample standard deviation, n is the sample size, and p is the proportion.

- Use the Confidence Interval formula above, and the correct formula for E, to and calculate the 95% confidence interval for any population mean of your choice. Write down (invent) the sample size (be sure it is 30 or above), the sample mean, and the sample standard deviation. Then, calculate the confidence interval. Remember, you are inventing all the values, so no two posts should look the same.
- Use the Confidence Interval formula above, and the correct formula for E, to and calculate the 95% confidence interval for any population proportion of your choice. Write down (invent) the sample size (be sure it is 30 or above) and the sample proportion. Then, calculate the confidence interval. Remember, you are inventing all the values, so no two posts should look the same.

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