One Proportion Test Help
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This test is performed with binary data when you want to examine the absence or presence of a specific attribute. This type of test is very common in elections when polling people to find out if they support person A or person B.
The test gives two options based on the size of the sample: large or small sample. A different approach is used based on which case is selected. You should select the large sample case when npbar > 10 where n = sample size and pbar is the average proportion of events.
You have the option for a hypothesis test based on a hypothesized proportion. You also have the option for a two-sided, lower one-sided or an upper one-sided test.
The One Sample Proportion Test input form is shown above. The data are entered directly into the input form. For example, consider the following example. A magazine conducted a telephone survey of 800 adults and asked if they had guns in the home. 45% of the respondents said yes. We want to develop a 95% confidence interval for the proportion of homes with guns. We also want a hypothesis test to see if 50% of the homes have guns. In this example, n = 800 and pbar = .45. Thus, n(pbar) =800(.45) = 360. We will use the large sample option.
- 1. Select “Sample Tests” from the “Statistical Tools” panel in the SPC for Excel ribbon.
- 2. Select the “One Proportion Test” option from the “Sample Tests” form. Select OK and the input form below is shown.
![](https://www.spcforexcel.com/wp-content/uploads/One-Proportion-Input.jpg)
- Title: enter the title of the test (optional).
- Number of Events: this is the number of events that occurred; in this example, the number of respondents who said they had guns in their house.
- Sample Size: this is the sample size; the total number of people survey in this example.
- Small or Large Sample: select the large sample size if npbar is greater than 10; select the small sample size if it is less than 10.
- Type of Test, Alpha: the input form below is displayed if this option is selected.
![](https://www.spcforexcel.com/wp-content/uploads/Type-of-Hypothesis.jpg)
- Select the Type of Test: two-sided; lower one-sided, or upper one-sided, the default is two-sided.
- Alpha: this is the confidence level; 1-alpha is the confidence interval, default is 0.05 or 95% confidence interval.
- Output Options: the input form below is displayed if this option is selected.
![](https://www.spcforexcel.com/wp-content/uploads/zt-Output-Options.jpg)
- First Cell of Output Range on this Worksheet: Select this option if you want the output on an existing worksheet; then select the first cell of the range where you want the output placed; a check is made to ensure that no existing data are overwritten in the worksheet.
- New Worksheet: Select this option if you want the results on a new worksheet.
- Enter Average, Sigma and Size: the input form below is displayed if this option is selected.
![](https://www.spcforexcel.com/wp-content/uploads/Summarized-Statistics-Two-Means.jpg)
- You many enter the sample size, standard deviation, or the average for processes 1 and 2; any value that is entered will be used in place of the values calculated from the data.
- Select OK to generate the results.
- Select Cancel to end the program.
One Proportion Test Output
The output from the One Sample Proportion Test is shown below. The entries are explained below the output.
![](https://www.spcforexcel.com/wp-content/uploads/One-Proportion-Output.jpg)
The output tells you the conclusion from the test. The null hypothesis (H0) and the alternate hypothesis (H1) are printed below the title.
- Sample Case: Sample case selected by user
- Number of Events: Number of events entered by user
- Sample Size: Sample size entered by user
- Sample p: Sample p = events/sample size
- Sample q: Sample q = 1 – p
- Alpha: Alpha entered by user
- z(0.025): Calculated z value based on alpha
- Lower Confidence Limit: 100(1-alpha)% upper confidence interval
- Upper Confidence Limit: 100(1-alpha)% lower confidence interval
- z: Calculated z value
- p Value: Calculated p value (in red if p value ? alpha)
A plot of the confidence interval is also given which shows the relationship of the confidence interval to the hypothesized proportion.
![](https://www.spcforexcel.com/wp-content/uploads/Hypothesized-Proportion.jpg)