The Thematic Apperception Test TAT presents participants wit

The Thematic Apperception Test (TAT) presents participants with ambiguous pictures and asks them to tell a story about them. These stories can be scored in any number of ways. Werner, Stabenou, and Pollin (1970) asked mothers of 20 normal and 20 schizophrenic children to complete the TAT, and scored the number of stories (out of 10) that exhibited a positive parent-child relationship. Assuming that TAT scores are a quantitative measure, calculate the 95% confidence interval for the difference in TAT scores.

Normal

Schizophrenic

8

2

2

0

4

1

1

2

6

1

1

4

3

4

3

2

1

3

2

3

4

3

7

3

4

2

2

0

6

6

1

1

4

3

3

2

2

4

1

2

Solution

alpha,a = 1-0.95 = 0.05
n1 = 20 , xbar1 = 3.55 , s1 = 1.877
n2 = 20 , xbar2 = 2.1 , s2 = 1.552

standard error, SE = sqrt((s1^2/n1)+(s2^2/n2))
SE = sqrt((1.877^2/20) + (1.552^2/20)) = 0.5446

degree of freedom,df = min(n1-1, n2-1) = 19

t(a/2,df) = t(0.025, 38) = 2.093

confidence interval:
(xbar1-xbar2) +/- [t(a/2,n1+n2-2) * SE]
(3.55-2.1) +/- [2.093 * 0.5446]
1.45 +/- 1.1398
( 0.3102 , 2.5898 )