# Methods and formulas for Bootstrapping for 1-Sample Mean

Select the method or formula of your choice.

## Average

### 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

### 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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