Standard Deviations	Sample Sizes	Assume Equal Standard Deviations (Pooled)	Do Not Assume Equal Standard Deviations (Not Pooled)
Study					T test statistic	Degrees of Freedom	P-value	T test statistic	Degrees of Freedom	P-value
1	12	10	20	20	1.431	38	0.1605	1.431	36.80	0.1607
2	12	10	50	50	2.263	98	0.0258	2.263	94.91	0.0259
3	6	5	20	20	2.863	38	0.0068	2.863	36.80	0.0069
4	6	6	32	8	2.108	38	0.0417	2.108	10.79	0.0593
5	8	6	20	20	2.236	38	0.0313	2.236	35.24	0.0318
6	8	6	10	30	2.097	38	0.0427	1.814	12.55	0.0937
7	8	6	30	10	1.808	38	0.0785	2.088	20.58	0.0494
8	12	2	20	20	1.838	38	0.0739	1.838	20.05	0.0809
9	12	2	10	30	2.246	38	0.0306	1.312	9.17	0.2216
10	12	2	30	10	1.301	38	0.2012	2.193	33.29	0.0354

What do we learn from this? Answer the following questions.

1. Compare Studies 5 - 10: (5 pts total)
   1. In which two of these studies does the assumption regarding the equality of the population standard deviations (i.e. pooling) have the greatest effect on the two p-values?
   2. Given the respective sample standard deviations of these studies, does it seem reasonable to assume the population standard deviations are equal (i.e. pool)?
   3. Question 3/study 3, shows how decreasing standard deviations effects p-values. In light of that insight, consider the two p-values of the 2 studies you selected: for which of these studies does pooling decrease the pooled standard deviation and for which does pooling increase it?
   4. Look closely at the sample standard deviations and sample sizes of your two studies and your answer to part c. How does pooling seem to handle two studies of differing sample sizes compared to the "Not Pooled" case?