6.[15 points total]The following table presents information on 4 different random samples from the same population. Imagine that each sample is investigating atwo-tailed null hypothesisthat the mean is79; and that thesample meanineachsample is80; and thestandard deviationineachsample is10. Some of the samples would reject the null hypothesis, other would not. Reportwhat this table is supposed to illustrate, andexplain what makes the illustrated phenomena occur.

The following table reports the test statistics corresponding to a single-sample test of the hypothesized mean computed from 4 different random samples of various sizes (with each sample having the same mean and standard deviation as reported above).

Sample size	Test Statistic (Z Obtained )
101	1.00
201	1.41
501	2.23
1001	3.16

a)[5 points]What does this table illustrate? Why doesn't the same sample mean provide the same testoutcome?

b)[10 points]What makes this phenomena occur.