Comparing z with s and t Figures
What is the difference between the z figures and the s figures, as well as the t figures? Why are they different?
To clarify the differences, can you explain what causes the variations in the z and t figures?
Answer:
When comparing the z with s figures and the t figures, the main difference lies in the distributions and critical values. The center of each interval is the same, but the widths of the intervals are larger using the t distribution than the z distribution with s.
The discrepancy in the widths of the intervals is due to the critical value for z, zα/2, being smaller than the critical value for t, tα/2,n-1. This difference in critical values affects the range of the t distribution, making it wider than that of the z-distribution.
Therefore, the main factor causing the difference between the z and t figures is the critical values and the number of samples used in the distribution.