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To calculate a confidence interval for the population mean (average), under these conditions, do the following: Determine the confidence level and degrees of freedom and then find the appropriate t*-value. Find the sample mean. Multiply t* times s and divide that by the square root of n
You estimate the population mean,
by using a sample mean,
plus or minus a margin of error. The result is called a confidence interval for the population mean,
In many situations, you don’t know
so you estimate it with the sample standard deviation, s; and/or the sample size is small (less than 30), and you can’t be sure your data came from a normal distribution. (In the latter case, the Central Limit Theorem can’t be used.) In either situation, you can’t use a z*-value from the standard normal (Z-) distribution as your critical value anymore; you have to use a larger critical value than that, because of not knowing what
is and/or having less data.
The formula for a confidence interval for one population mean in this case
is the critical t*-value from the t-distribution with n – 1 degrees of freedom (where n is the sample size).
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