Select the method of your choice.

The interval (PL, PU) is an approximate 100(1 – α)% confidence interval of p.

When *x* = 0 or *x* = n, Minitab calculates only a one-sided confidence interval.

Term | Description |
---|---|

v_{1} | 2x |

v_{2} | 2(n – x + 1) |

x | number of events |

n | number of trials |

F | lower α/2 point of F distribution with v_{1} and v_{2} degrees of freedom |

Term | Description |
---|---|

v_{1} | 2(x + 1) |

v_{2} | 2(n – x) |

x | number of events |

n | number of trials |

F | upper α/2 point of F distribution with v_{1} and v_{2} degrees of freedom |

Term | Description |
---|---|

observed probability, = x / n | |

x | observed number of events in n trials |

n | number of trials |

z_{α}_{/2} | inverse cumulative probability of the standard normal distribution at 1–α/2 |

α | 1 – confidence level/100 |

The sample (*X*) comes from binomial distribution with parameters *n* and *p*.

- H
_{1}:*p*>*p*_{o}, p-value = P{*X*>*x*|*p*=*p*_{o}} - H
_{1}:*p*<*p*_{o}, p-value = P{*X*<*x*|*p*=*p*_{o}} - H
_{1}:*p*≠*p*_{o}and*p*_{o}= 1/2, p-value = P{*X*<*y*or*X*>*n*–*y*|*p*=*p*_{o}}

Term | Description |
---|---|

n | number of trials |

p | probability of success |

x | observed number of successes |

y | min {x, n – x} |

Minitab uses the likelihood ratio test for:

H_{1}: p ≠ p_{o} and p_{o} ≠ 1/2

The likelihood function is defined as:

such that

LR (*x*) ≥ *c*

Minitab evaluates the likelihood ratio for all possible values of *X* = (0, 1,…, *n*) and sums the probabilities for all values for which the LR (*y*) ≥ LR (*x*).

- p-value = Σ P{
*X*=*y*|*p*=*p*_{o}}

Term | Description |
---|---|

c | critical value chosen to obtain the desired significance level, α |

x | observed number of successes |

y | min {x, n – x} |

n | number of trials |

Term | Description |
---|---|

observed probability, x/n | |

x | observed number of events in n trials |

n | number of trials |

p_{0} | hypothesized probability |