# 8.1.2.2.2 - Minitab Express: 1 Sample Proportion z test, Summary Data

8.1.2.2.2 - Minitab Express: 1 Sample Proportion z test, Summary Data

The following example uses a scenario in which we want to know if the proportion of college women who think they are overweight is less than 40%. We collect data from a random sample of 129 college women and 37 said that they think they are overweight.

First, we should check assumptions to determine if the normal approximation method or exact method should be used:

$np_0=129(0.40)=51.6$ and $n(1-p_0)=129(1-0.40)=77.4$ both values are at least 10 so we can use the normal approximation method.

## MinitabExpress – Performing a One Proportion z Test with Summarized Data

To perform a one sample proportion z test with summarized data in Minitab Express:

1. Open Minitab Express without data
2. On a PC: In the menu bar select STATISTICS > One Sample > Proportion
3. On a Mac: In the menu bar select Statistics > 1-Sample Inference > Proportion
4. From the drop-down menu change Sample data in a column to Summarized data
5. For Number of events enter 37 and for Number of trials enter 129
6. Check the box for Perform hypothesis test
7. In the Hypothesized proportion box enter 0.40
8. Click the Options tab
9. Change the Alternative hypothesis to Proportion < hypothesized value
10. Use the default Confidence level of 95
11. Change the Method to Normal approximation
12. Click OK

This should result in the following output:

1-Sample Proportion
 p: event proportion Normal approximation is used for this analysis.
Descriptive Statistics
N Event Sample p 95% Upper Bound for p
129 37 0.286822 0.352321
Null hypothesis H 0: p = 0.4 H 1: p < 0.4
Z-Value P-Value
-2.62 0.0043

Video Walkthrough

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

We could summarize these results using the five-step hypothesis testing procedure:

1. Check assumptions and write hypotheses

$np_0=129(0.40)=51.6$ and $n(1-p_0)=129(1-0.40)=77.4$ both values are at least 10 so we can use the normal approximation method.

$H_0: p = 0.40$

$H_a: p < 0.40$

2. Calculate the test statistic

From output, $z$ = -2.62

3. Determine the p-value

From output, $p$ = 0.0043

4. Make a decision

$p \leq \alpha$, reject the null hypothesis

5. State a "real world" conclusion

There is evidence that the proportion of women in the population who think they are overweight is less than 40%.

# 8.1.2.2.2.1 - Video Example: Gym Members (Normal Approx. Method)

8.1.2.2.2.1 - Video Example: Gym Members (Normal Approx. Method)

Research question: Are less than 50% of all individuals with a membership at one gym female?

A simple random sample of 60 individuals with a membership at one gym was collected. Each individual's biological sex was recorded. There were 24 females.

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