# 9.1.1.1 - Minitab: Confidence Interval for 2 Proportions

9.1.1.1 - Minitab: Confidence Interval for 2 Proportions

Minitab 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.

1. Open Minitab file: class_survey.mpx
2. Select Stat > Basic Statistics > 2 Proportions
3. Select Both samples are in one column from the dropdown
4. Double click the variable Try Weed  in the Samples box
5. Double click the variable Biological Sex in the Sample IDs box
6. Keep the default Options
7. 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 $$H_0$$: $$p_1-p_2=0$$ $$H_1$$: $$p_1-p_2\neq0$$
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.

1. Open Minitab
2. Select Stat > Basic Statistics > Two-Sample Proportion
3. Select Summarized data in the dropdown
4. For Sample 1 next to Number of events enter 92 and next to Number of trials enter 120
5. For Sample 2 next to Number of events enter 23 and next to Number of trials enter 160
6. Keep the default Options
7. 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 $$H_0$$: $$p_1-p_2=0$$ $$H_1$$: $$p_1-p_2\neq0$$
Method Z-Value P-Value
Normal approximation 13.10 0.000
Fisher's exact   0.000

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