Question

Comparing the "z with s" and the "t" figures, describe the difference between the two figures using the z distribution and the two figures using the t distribution. Please explain why they are different. In your response, be sure to indicate which option in the applet is causing the difference.

Answer 1

Answer:

The center of both the distribution are similar. However the range of the t distribution  is larger than that of the z-distribution.

Explanation:

The center of both the distribution are similar. However the range of the t distribution  is larger than that of the z-distribution.

This is because the critical values of z and zα/2 are less than that of  t and tα/2 by the value of n-1.

Thus the main effect is by the number of samples, For 1 sample the value of t and z is same.

Answer 2

Answer:

The center of each interval is the same. The widths of the intervals are larger using the t distribution than the z distribution with s. This is caused by the fact that the critical value for z, zα/2, is less than the critical value for t, tα/2,n-1.