# 9.1.1.1 - Minitab Express: Confidence Interval for 2 Proportions

9.1.1.1 - Minitab Express: Confidence Interval for 2 ProportionsMinitab Express can be used to construct a confidence interval for the difference between two proportions using the normal approximation method. Note that the confidence intervals given in the Minitab Express output assume that \(np \ge 10\) and \(n(1-p) \ge 10\) for both groups. If this assumption is not true, you should use bootstrapping methods in StatKey.

## MinitabExpress – Constructing a Confidence Interval with Raw Data

Let's estimate the difference between the proportion of females who have tried weed and the proportion of males who have tried weed.

- Open Minitab Express file:
- On a
**PC**: In the menu bar select**STATISTICS > Two Samples > Proportions** - On a
**Mac**:**Statistics > 2-Sample Inference > Proportions** - Double click the variable
*Try Weed*in the box on the left to insert the variable into the*Samples*box - Double click the variable
*Biological Sex*in the box on the left to insert the variable into the*Sample IDs*box - Keep the default
*Options* - Click OK

This should result in the following output:

Event: Try Weed = Yes |

\(p_1\): proportion where Try Weed = Yes and Biological Sex = Female |

\(p_2\): proportion where Try Weed = Yes and Biological Sex = Male |

Difference: \(p_1-p_2\) |

Biological Sex | N | Event | Sample p |
---|---|---|---|

Female | 127 | 56 | 0.440945 |

Male | 99 | 62 | 0.626263 |

Difference | 95% CI for Difference |
---|---|

-0.185318 | (-0.313920, -0.056716) |

Null hypothesis | \(H_0\): \(p_1-p_2=0\) |
---|---|

Alternative hypothesis | \(H_1\): \(p_1-p_2\neq0\) |

Method | Z-Value | P-Value |
---|---|---|

Fisher's exact | 0.0072 | |

Normal approximation | -2.82 | 0.0047 |

Select your operating system below to see a step-by-step guide for this example.

## MinitabExpress – Constructing a Confidence Interval with Summarized Data

Let's estimate the difference between the proportion of Penn State World Campus graduate students who have children to the proportion of Penn State University Park graduate students who have children. In our representative sample there were 120 World Campus graduate students; 92 had children. There were 160 University Park graduate students; 23 had children.

- Open Minitab Express without data
- On a
**PC**: In the menu bar select**STATISTICS > Two Samples > Proportions** - On a
**Mac**:**Statistics > 2-Sample Inference > Proportions** - Change
*Both samples are in one column*to*Summarized data* - For
*Sample 1*next to*Number of events*enter*92*and next to*Number of trials*enter*120* - For
*Sample 2*next to*Number of events*enter*23*and next to*Number of trials*enter 160 - Keep the default
*Options* - Click OK

This should result in the following output:

\(p_1\): proportion where Sample 1 = Event |

\(p_2\): proportion where Sample 2 = Event |

Difference: \(p_1-p_2\) |

Sample | N | Event | Sample p |
---|---|---|---|

Sample 1 | 120 | 92 | 0.766667 |

Sample 2 | 160 | 23 | 0.143750 |

Difference | 95% CI for Difference |
---|---|

0.622917 | (0.529740, 0.716093) |

Null hypothesis | \(H_0\): \(p_1-p_2=0\) |
---|---|

Alternative hypothesis | \(H_1\): \(p_1-p_2\neq0\) |

Method | Z-Value | P-Value |
---|---|---|

Fisher's exact | <0.0001 | |

Normal approximation | 13.10 | <0.0001 |

Select your operating system below to see a step-by-step guide for this example.