# 9.1.1.1 - Minitab Express: Confidence Interval for 2 Proportions

Minitab 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.

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

This should result in the following output:

2-Sample Proportions: Try Weed by Biological Sex
 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: $$p_1-p_2$$
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)
Null hypothesis $$H_0$$: $$p_1-p_2=0$$ $$H_1$$: $$p_1-p_2\neq0$$
Method Z-Value P-Value
Fisher's exact   0.0072
Normal approximation -2.82 0.0047 Video Walkthrough

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## 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.

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

This should result in the following output:

2-Sample Proportions
 $$p_1$$: 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)
Null hypothesis $$H_0$$: $$p_1-p_2=0$$ $$H_1$$: $$p_1-p_2\neq0$$
Method Z-Value P-Value
Fisher's exact   <0.0001
Normal approximation 13.10 <0.0001 Video Walkthrough

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