In the 1 Proportion test example, we have 92 students and 28 smokers in the group. The sample shows 30.4 percent of the group as smokers. The results from a 1 Proportion test will indicate that we cannot reject the null hypothesis.
For this recipe, we want to know how many students we need to sample in order to be able to observe a difference of 2.5 percent or 5 percent between the hypothesized and actual proportions that have a power of 80 percent. We will use a hypothesized proportion of 25 percent and differences of 2.5 and 5 percent.
The following steps will help us find the number of samples needed to identify a difference of 2.5 percent or 5 percent with at least an 80 percent chance of identifying this difference:
- Go to the Stat menu, click on Power and Sample Size, and select 1 Proportion….
- Enter
.25in the Hypothesized proportion: field. - Enter
.2 .225 .275 .3in the Comparison proportions: field and.8in the Power values: field. - Click on OK.
To achieve a power of 80 percent to observe a population with a different proportion to 0.25, we would require a sample size of over 2300 for a 0.025 difference or around 600 samples for a 0.05 difference.
We should also note that we require less samples for the same power to observe a decrease than an increase in the proportion. The results show us that we need 2305 samples to see a proportion of 0.225 or 2399 for a proportion of .275.
By specifying two of the values of Sample sizes:, Power values:, and Comparison proportions:, Minitab will calculate the third value. Each of these three fields will accept multiple values.
Try thinking about the difference that could be observed with only 300 surveyed students. This test can also be made more sensitive by changing the alternative from different to a one-sided test.