Question

3. Tai Chi is often recommended as a way to improve balance and flexibility in the elderly. Below are before-and-after flexibility ratings (on a 1 to 10 scale, 10 being most flexible) for 8 men in their 80's who took Tai Chi lessons for six months. Subject A B C D E F G H Flexibility rating after Tai Chi 2 | 4 3 3 | 3 | 4 | 5 10 Flexibility rating before Tai Chi 1 2 1 2 1 4 2 6 Do these paired data adequately meet the Normality condition for a t-procedure? Justify your answer. (2 points)

Answer 1

Let , Xi : Flexibility rating of the ith individual after Tai Chi

Yi : Flexibility rating of the ith individual before Tai Chi

Let , $d_i=X_i-Y_i$ for all i , i = 1(1)8

Xi	Yi	di
2	1	1
4	2	2
3	1	2
3	2	1
3	1	2
4	4	0
5	2	3
10	6	4

The normal probability plot of di is given below :

Normal probability plot for the differences Normal - -- --- --- --- --- --- --- --- --- --- Mean 1.875 11 StDev 1.246 - --- --- N AD 0.276 P-Value 0.552 ----- -- -nhanh-nhanh-h --- - Percent -- - . - - --- ---- -- -- -

For paired data , we want the distribution of the differences to be normal . The normal probability plot is almost linear with no visible outliers or skewness . Hence it meets the normality condition required for a paired t procedure .