Question

A pharmaceutical company claim that it new supplement possible to increase memory recall. Eight students from a large psychology class were selected at random and given 10 minutes to memorize a list of 20 nonsense words. Each was asked to list as many of words as he or she could remember in the next 24 hour later. The similar group of students consumes the supplement for a month and the test was repeated. Is there evidence to suggest that the mean number of words recalled after 1 hour exceeds the mean number of words recall after 24 hours by more than 3. Use significant level 0.1.

Subject	1	2	3	4	5	6	7	8
Before treatment	14	12	18	7	11	9	16	15
After treatment	10	4	14	6	9	6	12	12

Answer 1

Given

Before treatment

n1 = 8

Mean , x̄1 = 12.75

s1 = 3.694

After treatment

n2 = 8

Mean , x̄2 = 9.125

and

Here

s2 = 3.523

Here

: Mean number of the words recall after 1 hour

: Mean number of the words recall after 24 hour

H0 : - = 3

H1 :   - > 3

Test statistic , t = (x1-x2) - ( - ) / sqrt ( s1² / n1 + s2² / n2 )

t= (12.75-9.125) - 3 / sqrt ( 3.694² / 8+ 3.523²​​​​​​​ / 8 )

t = 0.625 / 1.8048

t = 0.3463

Degree of freedom = 8+8 -2 = 14

t-critical at and D.F =14 is 2.15

t < t-critical

So we reject H0.