# 8.1.1.2 - Minitab Express: Confidence Interval for a Proportion

8.1.1.2 - Minitab Express: Confidence Interval for a ProportionBefore we can construct a confidence interval for a proportion we must first determine if we should use the exact method or the normal approximation method. Recall that if \(np \geq 10\) and \(n(1-p) \geq 10\) then the sampling distribution can be approximated by a normal distribution. Since we don't have the population proportion (\(p\)), we using \(\widehat p\) as an estimate. Note that \(n\widehat p\) is the number of successes in the sample and \(n(1-\widehat p)\) is the number of failures in the sample.

If this assumption has not been met, then the sampling distribution is constructed using a binomial distribution which Minitab Express refers to as the "exact method."

To check this assumption we can construct a frequency table. You first learned how to construct a frequency table in Lesson 2.1.1.2.1 of these online notes. Here is another example:

## MinitabExpress – Frequency Tables

To create a frequency table of dog ownership in Minitab Express:

- Open the data set:
- On a
**PC**: In the menu bar select**STATISTICS > Describe > Tally** - On a
**Mac**: In the menu bar select**Statistics > Summary Statistics > Tally** - Double click the variable
*Dog*in the box on the left to insert the variable into the*Variable*box - Under Statistics, check
*Counts* - Click OK

This should result in the following frequency table:

Dog | Count |
---|---|

No | 252 |

Yes | 272 |

N= | 524 |

*= | 1 |

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

From the frequency table above we can see that there were at least 10 "successes" and at least 10 "failures" in the sample. In this example a success is defined as answering "yes" to the question "do you own a dog?" A failure is defined as answering "no." Because both \(n \widehat p \geq 10\) and \(n(1- \widehat p) \geq 10\), the normal approximation method may be used. In Minitab Express, the exact method is the default method. If there are at least 10 successes and at least 10 failures, then you need to change the method to the normal approximation method.

## MinitabExpress – Confidence Interval for a Proportion (Normal Approximation M

To create a 95% confidence interval of dog ownership using the normal approximation method in Minitab Express:

- Open the data set:
- On a
**PC**: In the menu bar select**STATISTICS > One Sample > Proportion** - On a
**Mac**: In the menu bar select**Statistics > 1-Sample Inference > Proportion** - In this case we have our data in the Minitab Express worksheet so we will use the default
*Sample data in a column* - Double click the variable
*Dog*in the box on the left to insert the variable into the*Sample*box - Click on the
*Options*tab - The default
*Confidence level*is 95 - Change the
*Method*to*Normal approximation*because the assumption of \(n \widehat p \geq 10\) and \(n(1- \widehat p) \geq 10\) has been met - Click OK

This should result in the following output:

Event: Dog = Yes |

p: proportion where Dog = Yes |

Normal approximation is used for this analysis. |

N | Event | Sample p | 95% CI for p |
---|---|---|---|

524 | 272 | 0.519084 | (0.476304, 0.561863) |

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

## What if the assumption is not met?

If the number of successes or the number of failures in the sample is less than 10, then the exact method should be used instead of the normal approximation method. In Minitab Express, this means that in step 8 above the default setting of *Exact method* should not be changed.

If you do not have a Minitab Express worksheet filled with data concerning individuals, but instead have summarized data (e.g., the number of successes and the number of failures), you would skip step 1 above and in step 3 you would select *Summarized data*. For *Number of events,* enter the number of successes (i.e., \(n \widehat p\)) and for *Number of trials* enter the total sample size (i.e., \(n\)).

# 8.1.1.2.1 - Video Example: Lactose Intolerance (Summarized Data, Normal Approximation)

8.1.1.2.1 - Video Example: Lactose Intolerance (Summarized Data, Normal Approximation)In a sample of 100 African American adults, 70 were identified as having some level of lactose intolerance. Compute a 95% confidence interval to estimate the proportion of all African American adults who have some level of lactose intolerance.