Confidence Intervals | Population Mean: σ Unknown

NOTE: Margin of error should be 1.6 (not 2.6).

For confidence intervals of the population mean: σ unknown, the main difference is that instead of using the z distribution, the t distribution is used. The t distribution is a family of probability distributions, with each individual t distribution depending on the degrees of freedom. Degrees of freedom refers to the number of independent pieces of information that go into computing the sample standard deviation. There are n-1 independent pieces of information because we know that the sum of the deviation about the mean is always equal to zero. Thus, we use n-1 degrees of freedom when computing confidence intervals for the population mean when the population standard deviation is unknown.

[SamSchaeffer]

Please check the math on the calculations. 2.672 x 4.4 / sqrt(54) = 1.599, round to 1.60. 22.5 +/- 1.60 = 20.90 to 24.10.

[veerakanneboina]

Why it is taken only alpha/2 in upper tail, why can't it be from alpha/2 of lower tail of the distribution