# Methods and formulas for Bootstrapping for 1-sample proportion

Select the method or formula of your choice.

## Proportion of the observed sample

When the chosen statistic is a proportion, Minitab displays the proportion from the observed sample.

### Notation

TermDescription
x number of events in the original sample
N number of trials in the original sample

## Average

### Formula

###### Note

Minitab does not take resamples from the original column of data. Instead, Minitab takes the resamples by randomly sampling from a binomial distribution. The parameters for the distribution are taken from the original sample.

### Notation

TermDescription
proportion of the ith resample
B number of resamples
N number of trials in the original sample

## P-Value

### Formula

The calculation of the p-value depends on the alternative hypothesis.
• Proportion less than hypothesized value:
• Proportion not equal to hypothesized value:
• Proportion greater than hypothesized value:
###### Note

In some cases, Minitab performs a one-sided test because the p-value for the two-sided test cannot be calculated. For more information, go to Why do I get a one-sided test instead of a two-sided test?.

### Notation

TermDescription
lnumber of bootstrap proportions that are less than or equal to the sample proportion
unumber of bootstrap proportions that are greater than or equal to the sample proportion
βnumber of resamples
nlnumber of bootstrap proportions that are less than or equal to ρ0d
nunumber of bootstrap proportions that are greater than or equal to ρ0 + d
ρ0hypothesized value
d
proportion of the observed sample