# 9.1.1.1 - Minitab: Confidence Interval for 2 Proportions

9.1.1.1 - Minitab: Confidence Interval for 2 ProportionsMinitab 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 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.

##
Minitab^{®}
– 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 file: class_survey.mpx
- Select
*Stat > Basic Statistics > 2 Proportions* - Select
*Both samples are in one column*from the dropdown - Double click the variable
*Try Weed*in the*Samples*box - Double click the variable
*Biological Sex*in the*Sample IDs*box - Keep the default
*Options* - Click OK

This should result in the following output:

##### Method

Event: Try_Wee = Yes

\(p_1\): proportion where Try_Weed = Yes and Biological Sex = Female

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

Difference: \(p_1\)-\(p_2\)

##### Descriptive Statistics: Try Weed

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

Female | 127 | 56 | 0.440945 |

Male | 99 | 62 | 0.626263 |

##### Estimation for Difference

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

-0.185318 | (-0.313920, -0.056716) |

*CI based on normal approximation*

##### Test

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

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

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

Normal approximation | -2.82 | 0.005 |

Fisher's exact | 0.007 |

##
Minitab^{®}
– 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
- Select
*Stat > Basic Statistics > Two-Sample Proportion* - Select
*Summarized data*in the dropdown - 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:

##### Method

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

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

Difference: \(p_1\)-\(p_2\)

##### Descriptive Statistics

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

Sample 1 | 120 | 92 | 0.766667 |

Sample 2 | 160 | 23 | 0.143750 |

##### Estimation for Difference

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

0.622917 | (0.529740, 0.716093) |

*CI based on normal approximation*

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

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

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

Normal approximation | 13.10 | 0.000 |

Fisher's exact | 0.000 |