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This is the idea behind the so called student t-test, a statistical tool for deciding if the mean of some sample is different from a population with a known mean. Conceptually, we want to consider two things:
How far above the mean are our samples?
How high is the variance in our sample?
Even if the mean of our sample is higher than the population mean, it's hard to know if this is random chance. But if the size of the difference is much larger than the noise in our sample, then we can confidently conclude that our sample has a higher mean.
The formula (that your calculator uses under the hood) is
where xˉ is the sample mean, μ the population mean, s the sample standard deviation, and n the number of samples.
This is the idea behind the so called student t-test, a statistical tool for deciding if the mean of some sample is different from a population with a known mean. Conceptually, we want to consider two things:
How far above the mean are our samples?
How high is the variance in our sample?
Even if the mean of our sample is higher than the population mean, it's hard to know if this is random chance. But if the size of the difference is much larger than the noise in our sample, then we can confidently conclude that our sample has a higher mean.
The formula (that your calculator uses under the hood) is
where xˉ is the sample mean, μ the population mean, s the sample standard deviation, and n the number of samples.