Video: Calculating Confidence Intervals

A sample of the heights of 𝑛 people from a population resulted in a sample mean of 𝑋 meters. Given that the standard deviation, 𝜎, is known, write an interval that represents a 90% confidence interval for the population mean.

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Video Transcript

A sample of the heights of 𝑛 people from a population resulted in a sample mean of 𝑋 meters. Given that the standard deviation is known, write an interval that represents a 90 percent confidence interval for the population mean.

For a population with an unknown mean 𝜇 and known standard deviation, a confidence interval for the population mean, based on a simple random sample of size 𝑛, is 𝑋 plus or minus 𝑍 times the standard deviation over the square root of 𝑛.

And we also need to know that a 90 percent confidence interval needs a 𝑍 value of 1.645. So an interval have a lower value and a higher value, the lowest and the highest.

So in order to find this confidence interval for the population mean, we must take the sample mean of 𝑋 minus the 𝑍 value of 1.645 times the standard deviation over the square root of 𝑛, the population size. And then, we take the exact same thing, except we use addition. That will give us the highest value.

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