Question

a dataset has sample proportions with a minimum of 0.20 and a maximum of 0.30 which bin width would allow for seeing the variabillity of the data in sampling distribution the options are 0.2 0.1 0.02 and 0.0002

Answer 1

To analyze a dataset with sample proportions ranging from 0.20 to 0.30, we want to select a bin width that allows for adequate visibility of the variability of the data in the sampling distribution.

Here are the options provided:

- 0.2
- 0.1
- 0.02
- 0.0002

**Analysis of Options:**
1. **0.2**: This bin width is too large relative to the range of the sample proportions (0.20 to 0.30). It would group all data points into a single bin, failing to show any variability.

2. **0.1**: This is still too wide, as it would create only one bin (0.20 to 0.30). Again, any variability in the data would be difficult to discern.

3. **0.02**: This bin width is much more appropriate. It would create several bins within the range (for example, 0.20 to 0.22, 0.22 to 0.24, etc.), thus allowing for a better view of variability in the data.

4. **0.0002**: While this is a very small bin width, it could lead to too many bins, potentially making it difficult to interpret the histogram. It does allow for the most granularity, but it might not be practical.

**Conclusion:**
The best option for seeing the variability of the data in the sampling distribution would be **0.02**. This width strikes a balance by being small enough to reveal variability while remaining manageable in terms of the number of bins generated.