Methods and formulas for Bootstrapping for 1-Sample Mean

Select the method or formula of your choice.

Average

Formula

Notation

TermDescription
mean of the ith resample
B number of resamples
N number of observations in the original sample

Standard deviation of the bootstrapping distribution

Formula

Notation

TermDescription
mean of the resamples
B number of resamples
mean of the ith resample

Confidence interval

Formula

Sort the means of the resamples in increasing order. x1 is the lowest number, xB is the highest number.

Lower bound: xl where =

Upper bound: xu where =

Note

For a one-sided case (only a lower bound or upper bound), use α instead of α/2.

When l or u are not integers, Minitab does a linear interpolation between the two numbers on either side of l or u. The formula is:

Xy + z(Xy+1 - Xy)

For example, if l = 5.25, the lower bound equals x5 + .25(x6 - x5).

Minitab does not display the confidence interval when or .

Notation

TermDescription
α 1- confidence level/100
B number of resamples
Xy the yth row of data when the data are sorted from least to greatest
y the truncated value of l or u
zl-y or u - y
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