8.1.2.2 - Minitab Express: Hypothesis Tests for One Proportion
8.1.2.2 - Minitab Express: Hypothesis Tests for One ProportionA hypothesis test for one proportion can be conducted in Minitab Express. This can be done using raw data or summarized data.
- If you have a data file with every individual's observation, then you have raw data.
- If you do not have each individual observation, but rather have the sample size and number of successes in the sample, then you have summarized data.
The next two pages will show you how to use Minitab Express to conduct this analysis using either raw data or summarized data.
Note that the default method for constructing the sampling distribution in Minitab Express is to use the exact method. If \(np_0 \geq 10\) and \(n(1-p_0) \geq 10\) then you will need to change this to the normal approximation method. This must be done manually. Minitab Express will use the method that you select, it will not check assumptions for you!
8.1.2.2.1 - Minitab Express: 1 Proportion z Test, Raw Data
8.1.2.2.1 - Minitab Express: 1 Proportion z Test, Raw DataIf you have data in a Minitab Express worksheet, then you have what we call "raw data." This is in contrast to "summarized data" which you'll see on the next page.
In order to use the normal approximation method both \(np_0 \geq 10\) and \(n(1-p_0) \geq 10\). Before we can conduct our hypothesis test we must check this assumption to determine if the normal approximation method or exact method should be used. This must be checked manually. Minitab Express will not check assumptions for you.
In the example below, we want to know if there is evidence that the proportion of students who are male is different from 0.50.
\(n=226\) and \(p_0=0.50\)
\(np_0 = 226(0.50)=113\) and \(n(1-p_0) = 226(1-0.50)=113\)
Both \(np_0 \geq 10\) and \(n(1-p_0) \geq 10\) so we can use the normal approximation method.
MinitabExpress – Conducting a One Sample Proportion z Test: Raw Data
Research question: Is the proportion of students who are male different from 0.50?
- Open Minitab Express file:
- On a PC: Select STATISTICS > One Sample > Proportion
On a Mac: Select Statistics > 1-Sample Inference > Proportion - Double-click the variable Biological Sex to insert it into the Sample box
- Check the box next to Perform hypothesis test and enter 0.50 in the Hypothesized proportion box
- Click the Options tab
- Use the default Alternative hypothesis setting of Proportion ≠ hypothesized value
- Use the default Confidence level of 95
- Select Normal approximation method
- Click OK
The result should be the following output:
Z-Value | P-Value |
---|---|
-1.86 | 0.0625 |
Event: Biological Sex = Male |
p: proportion where Biological Sex = Male |
Normal approximation is used for this analysis. |
N | Event | Sample p | 95% CI for p |
---|---|---|---|
226 | 99 | 0.438053 | (0.373368, 0.502738) |
Null hypothesis | H _{0}: p = 0.5 |
---|---|
Alternative hypothesis | H _{1}: p ≠ 0.5 |
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:
\(np_0 = 226(0.50)=113\) and \(n(1-p_0) = 226(1-0.50)=113\) therefore the normal approximation method will be used.
\(H_0: p = 0.50\)
\(H_a: p \ne 0.50\)
From the Minitab Express output, \(z\) = -1.86
From the Minitab Express output, \(p\) = 0.0625
\(p > \alpha\), fail to reject the null hypothesis
There is NOT evidence that the proportion of all students in the population who are male is different from 0.50.
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 DataThe 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:
- Open Minitab Express without data
- 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
- From the drop-down menu change Sample data in a column to Summarized data
- For Number of events enter 37 and for Number of trials enter 129
- Check the box for Perform hypothesis test
- In the Hypothesized proportion box enter 0.40
- Click the Options tab
- Change the Alternative hypothesis to Proportion < hypothesized value
- Use the default Confidence level of 95
- Change the Method to Normal approximation
- Click OK
This should result in the following output:
p: event proportion |
Normal approximation is used for this analysis. |
N | Event | Sample p | 95% Upper Bound for p |
---|---|---|---|
129 | 37 | 0.286822 | 0.352321 |
Null hypothesis | H _{0}: p = 0.4 |
---|---|
Alternative hypothesis | H _{1}: p < 0.4 |
Z-Value | P-Value |
---|---|
-2.62 | 0.0043 |
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:
\(np_0=129(0.40)=51.6\) 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.
\(H_0: p = 0.40\)
\(H_a: p < 0.40\)
From output, \(z\) = -2.62
From output, \(p\) = 0.0043
\(p \leq \alpha\), reject the null hypothesis
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.